THE ELEMENTS 



OF 



VITAL STATISTICS 



/ 

ARTHUR NEWSHOLME, M.D. lond., F.R.CP. 

EXAMINER IN STATE MEDICINE TO THE UNIVERSITY OF LONDON 

AND IN PREVENTIVE MEDICINE TO THE UNIVERSITY OF OXFORD 

UNIVERSITY SCHOLAR IN MEDICINE 

FELLOW OF THE ROYAL STATISTICAL SOCIETY 

MEDICAL OFFICER OF HEALTH OF BRIGHTON 




THIRD EDITION, ALMOST ENTIRELY REWRITTEN 



LONDON 

SWAN SONNENSCHEIN & CO., Lim. 

new vork: the mac.millan company 

iSqq 






\o 



51846 



INTRODUCTION. 



yITAL Statistics may be defined as the science of 
numbers applied to the life-history of communities 
and nations ; and in the following pages the chief statis- 
tical facts concerning the various phases and stages of life 
will be in turn presented. The subject naturally divides 
itself into two sections : first, the sources of information, ^ 
as the census enumerations, registration of births, marriages, \ 
sickness, death, etc. ; and second, the information derived 
from these sources, which will be discussed in detail in the 
following pages. (See table of contents, pages vii.-xii.) 

As the scope of a science widens, it is generally found 
necessary sooner or later to adopt numerical standards 
of comparison. In medical science this is found to be 
especially necessary, though perhaps in no other science 
is the difficulty of exact numerical statement so great. 
The value of experience, founded on an accumulation of 
individual facts, varies greatly according to the character 
of the observer. As Dr. Guy has put it : " The sometimes 
of the cautious is the often of the sanguine, the always of 
the empiric, and the never of the sceptic; while the num- 
bers 1, 10, 100, and 10,000 have but one meaning for all 
mankind." 

The variable accuracy of individual observers makes us 



iv VITAL STATISTICS. 

distrustful of generalities founded on imperfect reasoning 
or defective facts, and necessitates the use of figures. Ex- 
perience tells us that a certain event is to be expected, 
while the numerical method can tell us how often it is 
to be expected. It is sometimes said tliat statistics may 
he made to prove anything; and no doubt they may be 
manipulated in such a manner as to make it difficult to 
detect the fallacies involved in their abuse. But this 
ignorant or unscrupulous abuse of figures does not dis- 
credit their legitimate use, and that they have a very 
important and perfectly trustworthy application to medical 
facts will be abundantly shown in the following pages. 



PREFACE TO NEW EDITION. 



THE steady demand for this work since the lirst edition 
was published in 1889, and the numerous inquiries 
that I have during the last two years received as to when 
a new edition would be ready, sufficiently indicate that 
it has fulfilled a useful purpose among those for whom it 
was specially intended — viz. medical officers of health and 
medical practitioners studying for a diploma in public 
health — and that it may in the future be even more widely 
useful. I take this opportunity of expressing my thanks to 
many of the above, and to correspondents in the United 
States and in foreign countries, who have shown their 
interest in the book, and have made suggestions of improve- 
ments which have been utilized in the preparation of the 
present edition. 

The present edition forms an almost entirely new book, 
although its general plan remains as hitherto. It difi'ers 
from former editions in regard to both omissions and 
additions. Much fewer statistical tables are inserted, it 
being assumed that the reader has access to the last aimual 
report and annual summary of the English Eegistrar-General, 
as well as the last decennial supplement, on which an Eng- 
lish text-book of vital statistics must necessarily be based. 
A number of foreign statistical tables have been inserted for 



vi VITAL STATISTICS. 

comparative purposes, as these are much more difficult of 
access to most readers. The exact method of construction 
of a life-table has been given, so that any medical officer 
of health may be able, by means of the instructions here 
given, to form a local life-table. 

In various parts of the book will be found critical 
observations on commonly employed statistical methods, and 
discussions of problems of public health which lend them- 
selves to statistical treatment. These, it is hoped, will 
increase the interest and value of the book, and lead to 
local investigations of disease on similar lines. 

In a work involving such a mass of statistics it cannot 
be expected that no errors have crept in. It is believed, 
however, that these are very few. The author will be 
grateful for an intimation as to any such errors that may 
be detected. 

AETHUE NEWSHOLME. 

11, Gloucester Place, Beightok, 
April 25th, 1899. 



TABLE OF CONTENTS. 



CHAPTER I. 

POPULATIOX. 



Requirements of Correct Statistics — Censi;s Enumerations — Errors in 
Census Data — Estimates of Population — Registrar-General's Official 
Method — Criticism of the Official Estimates — Quinquennial Census 
— Effects of Migration on Population — Internal Migration — Migration 
between Urban and Rural Districts — Birthplaces of the Population 
— Trans-Oceanic Emigration . . ... 1 

CHAPTER II. 

Population from an International Standpoint . . . 15 

CHAPTER III. 

Registration of BiRrns and Deaths. 

History of Registration — Law as to Registration of Births — Registration 
of Births in Relation to Vaccination — The Law as to Registration of 
Deaths — Relation of Registrar to Medical Officer of Health— Still- 
bii'ths — Uncertified Deaths — Inquests — Recommendations as to Death 
Certification — Improvements in Registration required — Use made of 
Information furnished by Registration . . . . 19 

CHAPTER IV. 

Death Certification and Classification of Causes of 
Death. 

Registration of Causes of Death — Deaths from Ill-defined Causes — Lack 
of Uniformity of Nomenclature — Official Form of Death Certificate — 
Nomenclature and Classification of Diseases . . . . 29 



viii VITAL STATISTICS. 

CHAPTER V. 
Registration of Sickness. 

PAGE 

Varying Relation between Morbidity and Mortality — Attempts made to 
Register Sickness — Information available — Scope of Preventive Medi- 
cine — Proposals as to National Notification and Registration of Sick- 
ness — Notification under Factory and Workshops Act . . . 37 

CHAPTER VI. 

The Compulsory Notification op Infectious Diseases. 

History of Compulsory Notification — Provisions of the Infectious Disease 
(Notification) Act, 1889 — Notification under the Public Health (Lon- 
don) Act, 1891 — Advantages of Compulsory Notification — Effect of 
Notification on Zymotic Mortality — National Registration of Infectious 
Diseases— Suggestions as to Notification of Infectious Diseases . .47 

CHAPTER VII. 

Marriages. 

, Methods of stating Marriage-rates — Condition as to Marriage of the 
English Population — Higher Marriage-rate in Towns — Influence of 
National Prosperity on Marriage -rate — Decline of Marriage -rate — 
Marriage Calendar — Marriages and Re-marriages — Ages at Marriage — 
Marriage of Minors — Signatures in Marriage-registers . . . 57 

CHAPTER VIII. 

Fecundity of Marriage. 

Methods of estimating Fecundity — Age in Relation to Fecundity — 
Duration of Married Life — Fecundity in different Countries . .64 

CHAPTER IX. 

Births. 

Estimation of Birth-rate — Defects in Registration of Births — National 
and International Birth-rates — Birth-rate in Urban Populations — 
Influence of Social Position and National Prosperity — Causes of Decline 
in Birth-rate — Still-births — Proportion of Males and Females at Birth 
— Illegitimacy — Illegitimacy in England and in other Countries — The 
Malthusian Hypothesis — Natural Increase of Population . .71 



TABLE OF CONTENTS. ix 

CHAPTER X. 

Death-hates. 

PACE 

Estimation of Death-rate— Death-rates for Sliort Periods— Crude and 
Special Death-rates — Elfect of Movements of Population— Effect of 
Public Institutions — Official Corrections . . . . 85 



CHAPTER XI. 

Relationship between Birth-rate and Death-rate. 

Influence of Birth-rate on Death-rate— A High Birth-rate and a Low- 
Birth-rate may both be followed by a Low Death-rate— A Special 
Illustration of Relationship between Birth-rate and Death-rate . 92 

CHAPTER XII. 

Death-rates Corrected for Age and Sex-distribution. 

Influence of Age and Sex -distribution on Death-rate— Method of 
Correction for Age and Sex-distribution— Trustworthiness of General 
Death-rates — Instances of Necessity for Correction . . .102 

CHAPTER XIII. 

Male and Female Mortality at Different Ages. 

Death-rate at Age-periods— Effect of Sex on Mortality— Death-rates 
per Standard Million of Population . ... 115 

CHAPTER XIV. 

Infantile Mortality. 

Infantile Population — Infantile Mortality— Mortality of Infants in 
each Month of First Year— Healthy District Experience of Infantile 
Mortality— Causes of Death among Infants— Factors of Infantile 
Mortality— Influence of Industrial Conditions— Influence of Age of 
Parents— Infantile Mortality in different Countries— Effect of Ille- 
gitimacy—Insurance of Infants in Relation to Infantile Mortality 
—Relation between Birth-rate and Infantile Mortality— Effect of 
Density of Population . • . ... 120 



X VITAL STATISTICS. 

CHAPTER XV. 

Influence of Climatic and Social Conditions on 
Mortality. 

PACE 

Influence of Climate and Season — Seasonal Incidence of General Mor- 
tality, of Diseases of Respiratory Organs, and of Zymotic Diseases 
— Cyclical Changes— Effect of Race, Marital Condition, Sanitation . 136 

CHAPTER XVI. 

Density of Population and Mortality. 

Method of Calculating Degree of Aggregation of Population — Relation 
between Density and Mortality — Urban and Rural Mortality — Causes 
of High Mortality with Increased Density — The True Test of Density 
of Population — Effects of Higher Degrees of Density on Mortality — 
Peabody Block Dwellings — Back-to-back Houses . . . 153 

CHAPTER XVII. 

Occupation and Mortality. 

Classification of Occupations-r-Methods of Comparison between Occu- 
pations — Occupational Mortality stated as Death-rates in a Standard 
Population— Sources of Error in Occupational Statistics— Mortality 
in different Occupations — Occupational Mortality distributed accord- 
ing to Causes— Effects of Breathing Foul Air and Dust-laden Air- 
Effects of Chronic Lead Poisoning— Effects of Alcoholic Excess . 169 

CHAPTER XVIII. 

Mortality from Zymotic Diseases. 

Methods of Stating Zymotic Death-rate — Periodicity in Epidemic 
Diseases — Average Death-rates— Measles— Scarlet Fever — Diphtheria 
— Whooping-cough — Fever — Diarrhcea . . . . 185 

CHAPTER XIX. 

Small-pox and Vaccination. 

Small -pox Statistics — Small -pox in the Pre -registration Period — The 
Epidemic of Small-pox of 1870-73— Small-pox in other Countries- 
Altered Age-incidence of Small-pox Mortality — Altered Age-incidence 
of other Diseases — Local Variations in Age-incidence of Small-pox 
— Fatality of Sniall-pox^Attack-rate among Vaccinated and Uu- 
vaccinated— Summary of Conclusions of Royal Commission . . 208 



TABLE OF CONTENTS. 

CHAPTER XX. 

Mortality fkom Certain Infective Diseases. 



I'AOE 



Definition of Puerperal Fever — Fallacious Methods of stating Mortality 
from Puerperal Fever — Tubercular Diseases — Possible Alterations in 
Nomenclature — Local Distribution of Phthisis . . .231 

CHAPTER XXI. 

Mortality from Cancer and Certain other Causes. 

Cancer Mortality at different Ages — Has Cancer Mortality really In- 
creased ? — Confusion between Deaths and Death-rates— Application 
of Graphic Method to Average Death-rates from Cancer — Local 
Distribution of Cancer — Heredity in Cancer — Diabetes — Dietetic 
Diseases — Developmental Diseases — Diseases of Nervous, Circulatory, 
and Urinary Systems— Violence — Suicides in different Countries . 241 

CHAPTER XXII. 

Life-Tables. 

Dr. Farr's Biometer — The Vision of Mirza— Description of Life-table 
— Method of Construction — Application of Graphic Method — Method 
for Ages under 5 — Curtate and Complete Expectation of Life . . 255 

CHAPTER XXIII. 

Abbreviated or "Short" Methods of Constructing 
Local Life-tables. 

Complete description of Method — History of Life-tables — De Moivre's 
Hypothesis — Price's Northampton Table— Milne's Carlisle Table — 
English Life-tables— Healthy Districts Life-tables — Other Life-tables 279 

CHAPTER XXIV. 

Methods of Calculating the Duration of Life. 

Connection between Mean Age at Death, Expectation of Life, and 
Number out of which One Dies Annually — Mean Age at Death — 
Effect of Birth-rate upon Mean Age at Death — Mean Length of 
Life — Mean Age of Living — Probable Duration of Life— The Mean 
Duration of Life — Expectation of Life or Mean After-lifetime — 
Formula of Willich, Bristowe, and Farr — Probabilities of Life . 290 



VITAL STATISTICS. 

CHAPTER XXV. 

Changes in the English Expectation of Life. 



PAGK 



Suiumary for England and Wales — Effect on Various Ages — Healthy 
Districts Experience — Life Capital . ... 304 

CHAPTER XXVL 

The Decline in the English Death-eate and its Causes. 

Distribution of the Decline at Various Ages — Discussion of Absence of 
Diminution at Higher Ages — Distribution of Decreased Mortality 
according to Cause . . . ... 314 

CHAPTER XXVIL 

Statistical Fallacies. 

Errors already Exposed — Classification of Fallacies — Errors from 
Paucity of Data — Errors from Inaccui'acy or Incompatibility of Data 
— Errors in comparing Total Deaths in successive Years — Errors in 
regard to Averages — Errors in connection with Average Strength — 
Fallacies of Hospital Statistics — Errors from the Composition of 
Ratios— Fallacies from stating Deaths in Proportion to Total Deaths 321 

CHAPTER XXVIIL 

Statistics of Sickness. 
Notification Returns — Friendly Societies . ... 337 

CHAPTER XXIX. 

Miscellanea. 

Graphic Methods — Means and Averages — Fatality or Case-mortality — 
Probability of Recurrence of a Disease apart from Infection — Calcu- 
lation of Population of Sub-Districts — Aids to Calculation . . 341 



VITAL STATISTICS. 



CHAPTER I. 

POPULATION. 

^nO obtain coriect and complete vital statistics it is essential 
JL to have (1) a correct enumeration of the population classified 
according to age, sex, occupation, etc.; and (2) a complete and ' 
accurate registration of l)irths and deaths and other important 
events in the life-history of individuals, as marriages and sickness, 
classified on the same basis as the statistics of population. 

An accurate estimate of population is the first desideratum, 
for population forms the natural basis of all vital statistics. In 
comparing different communities it is necessary to state the deaths\ 
and other statistical data in terms of the population, otherwise no ' 
true comparison can be instituted. 

The actual population is known only by census enumerations. 
For the years intervening between two census enumerations esti- 
mates of the population are made. 

The first complete census of modern times was taken in the N 
year 1751 in Sweden. In England the first census was in 1801, ' 
and then decennially, the tenth being taken on April 6tli, 1891. 
The first census, in 1801, showed the number of males and females 
of each house and family, and the occupation, classified roughly 
as agricultural, trading, and others not comj^rised under these two 
heads. In 1821 information was first sought as to ages, but it 
was left optional whether this information should be furnished or 
not. The first census which could be described as fairly complete 
was that of 1851, which was organized under Dr. Farr's super- 
vision. It obtained information as to occupation, birthplace, 
relationship (husband, wife, etc.), civil condition (married, widow, 



2 VITAL STATISTICS. 

bachelor, etc.), and the number of persons deaf and dumb or 
bhnd. At this census, under the powers given by the Census 
Act, the precise age at last birthday of each person in the country 
was first demanded. 

In the census report of 1881 the age and sex distribution 
of the population of each urban and rural sanitary authority, as 
constituted that year, was given for the first time. 

At the census of 1891 the schedule contained such new topics 
of inquiry as the number of rooms and of their occupants in all 
tenements Avith less than five rooms, and the important occupa- 
tional distinction between masters and men, and those working on 
their own account and without subordinates. 

Errors in Census Data. Ignorance of adults as to their precise 
age. Many adults are ignorant of their exact age. Dr. Ogle 
states that " not improbably the greater number of adults do not 
know their precise age, and can only state it approximately."* 
There is a great tendency to return ages as some exact multiple of 
ten, when really a year or two on one side or other of the precise 
figure (30, 40, 50, etc.). For this reason decennial age-periods are 
preferable in calculating death-rates, and 25-35, 35-45, etc., should 
be chosen in preference to 30-40, 40-50, etc. This tendency 
does not appear until adult Hfe, and quinquennia can therefore be 
safely used up to the age of 25 years. The ignorance of many 
adults as to their exact age and the consequent concentration 
on multiples of ten is clearly shown in Fig. l.t 

Untrustworthiness of Ages of Young Children. Among children 
under 5 years of age the vagueness with which parents use the 
terms "one year old," "two years old," etc., when the children 
are only in their first or second year respectively, is a cause of 
considerable error. 

Wilful Misstatement of Age occurs more especially among women; 
thus at every census the young women of 20 to 25 years of age 
have invariably been more numerous than were the girls aged 10 to 
15 at the immediately preceding census. This is clearly brought 

* Dr. Ogle's General Census Report, 1891, vol. iv. p. 27. For further 
particulars on this subject Dr. Ogle's report, which is summarised above, 
should be consulted. „,^ , oo 

t Taken from a paper by Mr. R. H. Hooker, m.a., on "Modes of (>ensus 
Taking in the British Dominions," Jour. Royal Statist. Soc, June, 1894. 



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4 VITAL STATISTICS. 

out in Fig. 2, * which shows the much greater excess of females 
over males aged 20 to 30, even after allowance is made for the 
fact that many men of those ages are abroad. 

The Tendency of Old Persons to Overstate their Ages throws 
some doubt on the figures for ages over 85, and it is preferable to 
make a single group for all ages over 85. 

5 10 20 25 30 35 40 45 50 55 60 65 70 75 SO 85 90 




110,000 
100,000 
90,000 
80,000 
70,000 
60,000 
50,000 
40,000 
30,000 
20,000 
10,000 



Fig. 2. — Excess of Females over Males at each. Age at the Census of 
England and Wales, 1891. 

Physical Infirmities are apt for obvious reasons to be understated. 
The schedule confines itself to blindness, deafness, and mental 
derangement, but in respect of all three the difficulty of fixing a 
standard of degree of impairment necessitating a return, as well 
as the general unwillingness of persons to admit the existence of 
any serious infirmity, make the results very inaccurate. 



From Mr. Hooker's paper, Jour. Statist, Soc, vol. Ivii. part ii. p. 348. 



POPULATIOIsL 5 

The most serious error, however, occurs in regard to occupaiions. 
Thus master and servant are commonly confused. In the census 
schedule of 1891 three new columns were placed, headed respec- 
tively " employer," " employed," and " neither employer nor 
employed," but the results obtained from this attempt at classifi- 
cation are regarded by Dr. Ogle as very untrustworthy.* 

Estimates of Population require to be made in the intervals 
between each census and the next succeeding one. Several 
methods of varying accuracy have been proposed. 

1. The natural increase, that is, the excess of births over deaths 
since the last census, being known, it would theoretically be possible, 
if one knew the amount of emigration and immigration, to state . 
the population in any given year. In this country accurate infor- 
mation as to migration has not hitherto been available ; and it is 
difficult to conceive that such information can ever become avail- 
able under modern conditions of life in respect of the inter- 
migration which occurs between the communities in different parts 
of the country. 

2. The population at the census enumerations in April, 18S1 
and 1891, being known, it is assumed that the rate of increase is 
in aritlimetical progression ; i.e., that the same annual increase 
continues during each year. Thus, given a population in April, 
1881, of 32,000, in April, 1891, of 36,000, to find the mean 
population in 1898. 

36000-32000 ,^^ , . 
— = 400 = annual nicrease. 

= 100 = increase from April to Midsummer. 

4 

Therefore mean population in 1898 = 36000 + 400 x 7 + 100 
= 38900. 

This method is most fallacious, as it makes no allowance for 
the increased number of parents year by year, owing to steadily- 
increasing numbers Avho year by year attain marriageable age. It 
assumes, in other words, simple interest when compound interest 
is really in action. 

3. The Registrar-General's method, the one generally adopted, 
assumes that the same rate of increase will hold good as in the 

* Census Report, 1891, vol. iv. p. 36. 



6 VITAL STATISTICS. 

previous iutercensal period, that is, that the population increases 
in geometrical pr'ogression. 

The problem is therefore one in compound interest. 
Let the net annual rate of increase per unit of population be 
represented by r. Then 1 at the beginning of a year will be 1 + r 
at the end of the same year or the beginning of the next year. 
Similarly, if the same rate of increase continue, the 

population at the end of the 2nd year = (l +r)2, 

„ „ 3rd year = (l+r)3, 

,, ,, ,, ?«th year = (l + r)re. 

If we commence with population P, the population at the end 
of the nth. year = P(l +r)". 

The value of r can be ascertained if avb know the population at 
the two last consecutive census enumerations. 

Thus if P' = population at the census 1891, 
P^ „ „ „ 1881, 

P^=P(l+7-)10. 

Taking the logarithm of each side of the equation, 
log. P = log. P + 1 log. ( 1 + ?•), 
.-. log. (l+r) = ^Vaog-^-log. P). 

Whence 1 + r is easily obtained from a table of logs. 
For example, if the census population of a town is 32,000 in 
1881, and 36,000 in 1891, what is the mean population in 1895 1 

(a) First find the rate of increase in 1881-91. 
Here P= 32000, P = 36000, 
log. P = log. 36000 = 4-556303, 
log. P =log. 32000 = 4-505150, 
log. P-log. P= -051153, 
Jjy (log P' - log P) = -0051 153 = log. 1 +T. 

(J)) Apply this to the increase in the next 4| years. 
HereP-P(l+r)V' 

(1895) (1891) 

log. P = log. 36000 + L7 log. (1 4 r), 

(1895) 

= 4-556303 + V- (-0051153), 
= 4-556303 + -0217400, 
= 4-578043. 

And from the table of logs, the population corresponding to 
this number = 37848 - population at the middle of 1895. 



POPULATION. 7 

It must be remembered that tlie mean j^)opulation of the year is 
taken as the basis of calculation of mortality and other rates, 
Avhich involves an estimate, even in the census year, for the three 
months between the census and midsummer. It would therefore 
be advantageous to have the census enumerations at the end of 
June as well as to have them more frequently. 

4. The results obtained by the last method may be to some 
extent chcclced for any given district by ascertaining the number 
of inhahifed houses for the year from the assessment books, and 
then multiplying this by the average number of inhal)itants in 
each house, as ascertained at the last census. This method, 
although it forms a useful check on the preceding method, in- 
volves the fallacy that new houses may be of a different class from 
those previously in existence, and may therefore have a diflerent 
number of occupants. 

5. If we assume that the Inrth-rate per 1000 inhahitants remains 

fairly constant, an additional means of checking the population is 

obtained. The number of registered births in a district in a given 

year being known, it is only necessary to calculate the population 

on the basis of the birth-rate knoAvn to have held good during the 

last census year. This method is becoming less reliable, owing to 

the decline in the birth-rate. In 1895 the birth-rate in England 

and Wales Avas 30'4, as compared Avith 31-4 in 1891. The 

number of births registered in England and Wales in 1895 having 

been 922,291, the population in that year, on the basis of the 

birth-rate in 1891, Avould be 

922291 X 1000 

y^^^yi X luuu ^ 29373248, 

Avhereas the estimated population based on the Eegistrar-General's 
method of calculation (page 6) Avas 30,383,047. The birth-rate, 
hoAvever, still gives a valuable clue to errors in the estimated 
populations of large toAvns. If the deviation from the birth-rate 
of the preceding ten or fifteen years is greater in any given year 
than in the immediately preceding years, there is strong reason for 
suspecting that the estimate of population is incorrect, unless 
great changes in the industrial condition of a community can be 
adduced in explanation of the anomaly. 

Similar objections may be urged against estimates based on 
returns of school-attendance, as the projDortion of children at 
school-ages Avill folloAV the births of preceding years. 



8 VITAL STATISTICS. 

Criticism of the Official "Estimates." Tlie assumption that 
the same rate of increase holds good in two successive decennial 
periods appears to be, under present conditions in this country, 
the least unsatisfactory basis for estimation of the population 
in an intercensal year. But it frequently gives unsatisfactory 
results, whether applied to the whole country, or to particular 
communities in it. Thus the decennial rate of increase of the 
English population in the ten periods elapsing since the first 
census in 1801 has been 14-0, 18-1, 15-8, 14-5, 12-9, 11-9, 13-2, 
14-4, and 11-6 per cent, respectively. Had the rate of increase in 
1881-91 remained as in 1871-81 the population of England 
aujd Wales would have increased from 25,974,439, in 1881, to 
29,704,468, instead of to 29,002,525, the population enumerated 
in 1891. The figures for great towns bring out much more 
strikingly the errors that may arise from the assumption that 
the same rate of increase continues as in the previous decennium. 
Thus at the census of 1891 the population of Salford Avas found 
to be 20'9 per cent, below the estimate "based on the rate of 
increase in 1871-81 ; that of Liverpool 16-6 per cent., and of 
ISTottingham 15 '6 per cent. beloAV the corresponding estimate; 
while at the opposite extreme the population of ISTewcastle-upon- 
Tyne was 13'6 per cent, above, and of Portsmouth 10-9 per cent, 
above the estimate. The above are extreme instances ; but the 
method is open to objection, even when the error is of smaller 
magnitude. The proper remedy is more frequent enumerations of 
population. 

A Quinquennial Census Avould go far to remedy the present 
uncertainties. Such a census is practised in France and Germany 
(triennial in some German states), in JSTew Zealand, Queensland, 
^lanitoba, and the North-Western territory of Canada, as well as 
in many of the states and several territories of the American 
republic. It is true that there are not as powerful reasons for 
a quinquennial census as on the Continent, where it is required 
for military purposes ; nor is there the same necessity as in many 
American states, where the increment of population is by leaps 
and bounds, and not steadily, as in most parts of our own country. 
Still, however, there are very strong reasons why a quinquennial 
census should be adopted, the chief one being that comparative 
vital statistics depend for their accuracy on estimates or enumer- 
ations of population, and that estimates necessarily become less 
trustworthy the more remote they are from enumerations. 



POPULATION. 



Vital statistics furnish the basis on which sanitary reforms rest, 
(-■specially in regard to legislation. Dr. Farr may in this sense be 
called the father of sanitary science. There are also political 
reasons for a quinquennial census, as political representation for 
both imperial and local purposes is likely to be based in future on 
a more strictly numerical basis. In addition, a more frequent 
census would lead to the work l^eing better done, owing to less 
diiliculty in collecting a sufiicient staff of intelligent enumerators 
and greater experience on tlieir part. The chief objection is the 
expense of the enumeration. In 1881 the census for Great 
Britani and Ireland cost ai)proximately £185,000, or about five 
guineas per 1000 of enumerated population. There is little 
doubt that this expense of each enumeration might be reduced by 
more frequent enumerations, but if not, the value of the results 
obtained would abundantly justify the double expenditure on 
the present basis. In the report presented to both Houses of 
Parliament in 1890 by the Committee appointed by the Treasury 
to inquire into certain questions connected with the taking of the 
census, it was recommended " that the number of the population 
and its distril)ution as regards age and sex be ascertained midway 
between the decennial periods at which a full census is taken," 
but unfortunately this recommendation has not been acted upon 
in 189G, except for London, on the initiative of the London 
County Council. This intermediate London census is rendered 
much less valuable by the absence of information as to the age 
and sex of the popidation. 

Effects of Migration on Population. The relative effect of 
the two factors governing the increase of population in England — 
natural increase and migration — may be seen from the following 
figures from the Census Report, 1891, vol iv. pp. 5-6 : — 













Difference, 












being loss or 








Gain per cent. 


Gain per 

cent, as 

determined 

by Actual 

Enumeration 


gain by excess 


Intercensal 
Period. 


Increase per 
cent, by 
Births. 


Decrease per 
cent, by 
Deaths. 


by excess of 

liirths over 

Deatlis, or 

Natural 


of Emigration 

over 

Immigration, 

or of 








Increase. 




Immigration 

over 
Emigration. 


1841-51 


34'64 


23-73 


10-91 


12-89 


+ 1 98 


1851-61 


36-19 


23-58 


12-61 


11-93 


-0-68 


1861-71 


37-56 


23-98 


13-58 


13-19 


-0-39 


1871-81 


37-89 


22-80 


15 09 


14-36 


-0-73 


1881-91 


34-24 


20-27 


13-97 


11-66 


-231 



10 VITAL STATISTICS. 

With the exception of the first period the natural increase was 
greater than the actual increase of population, and emigration was 
in excess of immigration. The decline of natural increase in 1881- 
91, as compared Avith 1871-81, is due to a lowered birth-rate and 
not to increased mortality, the mean annual death-rate in 1881-91 
having been loAver than in any earlier decennium on record. 

It is unfortunate that there are no accurate means of deter- 
mining in Avhat degree the increased loss by excess of emigrants 
over immigrants in 1881-91 Avas due to increased emigration, 
or in Avliat degree, if any, to diminished immigration.* In Ireland 
there is a special machinery for collecting emigration returns, and 
from these returns, combined with the balance of births over 
deaths, an estimate very near the truth can be obtained. 

Internal Migration. In urban districts Avith fixed boundaries 
the assumption that the rate of increase of the preceding decen- 
nium Avill continue becomes less accurate in proportion to the 
extent in Avhich the area of the districts in question becomes 
covered by houses. Thus the population of the County of 
London increased at the rate of 17'2 per cent, in 1871-81, at the 
rate of 10 '3 per cent, in 1881-91. It is highly improbable that 
the increase of the next decennium Avill approach 10 per cent., 
the population having extended in a centrifugal manner, and 
overstepped the geographical boundaries of the County of London. 
The present anomalies of parochial parishes, federated into registra- 
tion districts, Avhich often do not coincide Avith county boundaries, 
require adjustment. It may happen, as in the preceding instance 
and in many similar instances for other large toAvns, that in 
refusing to extend the statistical area of a toAAar Avhose population 
is rapidly overstepping the municipal boundaries, an area AAdiich 
once included the Avhole of a toAA'n finally includes only its centre, 
the statistics of the suburbs of the toAvn being arbitrarily separated 
from those of the centre to Avhicli they normall}'^ belong. 

Migration between Urban and Rural Districts. It is difficult 
to frame a definition Avhich shall satisfactorily distinguish between 
urban and rural districts. Many small toAvns, Avhich form the 
centres of agricultural districts, and Avhich have no important 
industries apart from that of the rural population surrounding 
them, are really rural, and not urban in their characteristics. Dr. 

* See a paper by Mr. E. Cannan, m.a., Jour. Royal Statist. Soc, vol. Ixi. 
part i. ' 



POPULATION. 11 

Ogle (Ci'itiiu.^ llrjjorf, 1891, p. 10) i)rnpo.ses two lines of arbitrary 
Jivisi(jn. In the first a po])ulation of 10,000, and in the second 
of 5000, constitutes the point at which a town ceases to come 
under the rural category. According to tlie first of these standards 
the urban po]iuIation had grown by 16'o4 per cent, between 1881 
and 1891, wiiile the remaining population had increased by only 
4*57 per cent. According to the second of these standards the 
urban ])oindation had increased l)y 16'05 i)er cent., the remaining 
population by 3"29 per cent. If the Local Government divisions 
into urban and rural sanitary districts be taken, the corresponding 
increase of urban po})uIati()U was 15'4 per cent., of rural popula- 
tion 2'98 per cent. 

Thus, whichever standard is adopted, there has been no literal 
depopulation of rural districts, but only a smaller rate of increase 
than in urljan districts. Somewhat varying results are obtained 
when Ave classify the counties according to the percentage decrease 
in rural population between 1881 and 1891. The greatest decrease 
is shown in Montgomeryshire (11 '68 per cent.), Cardiganshire 
(9 "20 per cent.), Radnorshire (7 '58 per cent.), and Flintshire 
(7*01 percent.). Twelve English and eight Welsh counties, out 
of the total 54 (including the three divisions of Yorkshire), show 
decreases. The only English C(junties of any numerical importance 
which show more than a trifling decline of rural population are 
Lincolnshire (4'29 per cent.), North and East Ridings of Yorkshire 
(4-62 and 2-41 per cent.), Cornwall (3-76 per cent.), Bedfordshire 
(2-55 per cent.), and Wiltshire (2'14 per cent.). 

As illustrative of the migration townwards may be adduced the 
fact that while in 1801 for every 100 persons in England and 
Wales there were 10-78 persons in London, this number had in- 
creased in 1891 to 14-52. 

The fact tliat the population of towns in every country is largely 
replenished from rural districts is shown by the following figures.* 
Out of a thousand inhabitants in each of the following cities the 
number of native-born persons was as follows : — 

. 425 

. 424 

. 424 

. 416 

. 349 

. 345 

• "The Laws of Migration," by Mr. E. G. Ravenstein, Jour. Statist. 
Soc, June, 1889. 



Antwerp . 


. 661 


Christiania 


London . 


. 629 


Budapest . 


Hamburg. 


. 543 


Berlin 


Copenhagen 


. 524 


Stockhohn 


Glasgow . 


. 513 


Paris 


Milan 


. 484 


Vienna 


Rome 


. 446 





12 VITAL STATISTICS. 

The general result is that towns and manufacturing districts 
everywhere grow more rapidly than rural districts. " This is a 
necessary consequence of the rigidly limited amount of land 
available for agriculture, and the practically unlimited amount of 
material available for manufacturing processes." * 

Dr. LongstafF has investigated the same subject from an inter- 
national standpoint,! and shows that "for the last forty years in 
every country throughout the world, new and old alike, the towns, 
and especially the large towns, have increased in population more 
rapidly than the rest of the country. . . . The causes, whatever 
they may be, affect alike Celt and Anglo-Saxon, Teuton, Latin, 
and Magyar." There can be little doubt that one chief cause of 
this tendency for the population to aggregate in towns is the 
greater pleasure and excitement enjoyed by toAvnspeople. Dr. 
Longstaff points out that improved communications are the chief 
exciting cause which render this greater urban aggregation practi- 
cable. With the improved means of locomotion must be associated 
the enormously increased use of machinery in every department of 
industry. The fact that corn can now be brought from Canada or 
Russia cheaper than it can be produced in England, tends to the 
same result. Gradually each country is becoming readjusted to 
produce the greatest amount of material at the expenditure of the 
smallest amount of labour, Avhether it be corn or manufactured 
goods, and the improved means of communication, national and 
international, enable this to be done, almost irrespective of distance, 
and determine the preponderance of urban or rural population. 

Birth-Places of the Population. The statistics as to birth- 
places of the population throAV much incidental light on the 
question of migration. Thus at the two last enumerations, out of 
every 10,000 persons in England and "Wales enumerated there were — 



Birth-place. 






In 1881. 


In 1891 


Enfjland and Wales . 






9,570 


9,614 


Scotland 


» 




98 


97 


Ireland 






216 


158 


Islands in British Seas 






11 


11 


British Colonies or Deper 


idencies 




36 


38 


Foreign parts (British 


snbjects 


and 






foreigners) . 






67 


80 


At sea . . . 






2 


2 



10,000 10,000 

* Dr. Ogle on "The Alleged Depopulation of the Rural Districts of 
England," Jour. Statist. Soc, June, 1889. 

t "Rural Depopulation," Jour. Statist. Soc, Sept., 1893. 



POPULATION. 13 

f 

Of the 29,002,525 persons enumerated, in this country at the 
last census 961 per 1000 were natives of England and Wales. 
In only nine counties was the actual growth, as shoAvn on 
enumeration, in excess of the natural growth by excess of births 
over deaths.* Of the natives of England and Wales who were 
in the country at the date of the census 74'86 per cent, were 
enumerated in their native counties, as compared with 74"04 per 
cent, in 1871. Thus altliough emigration to foreign countries 
increased enormously between 1881 and 1891, there was, not- 
withstanding increased facilities of communication and greater 
knowledge as to the conditions of life in parts outside their 
innnediate localities, no corresponding increase of inter-migration 
within the borders of England and Wales. 

The proportion of Irish in the English population had declined 
by 18 '5 per cent, between 1881 and 1891. This has been 
associated with a gradual decline in the population of Ireland 
itself. The proportion of Irish in England and Wales to Irish in 
their own country increased with each census up to 1881 and 
then declined. Thus in 1841 there were 36 Irish in this country 
to 1000 in Ireland itself; in 1851 there were 80; in 1861 there 
Avere 105 ; in 1871 there were 107 ; in 1881 there were 111 ; in 
1891 there were 100 to every 1000 in Ireland. 

The Scotch element in the English population has increased 
steadily from 6-5 per 1000 in 1841 to 98 per 1000 of the total 
population of England in 1881. 

Trans-Oceanic Emigration. Mr. Geoffrey Dragef quotes the 
trans-oceanic emigration statistics drawn up by Signer Eodio for 
all European countries during the period 1880-92, and comparing 
these with the enumerated populations of the same countries for 
the years 1889-91, obtains the following estimate of the proportion 
per 1000 lost by the various countries : — 

Country. 

Norway . 
United Kingdom 
Sweden 
Portugal . 
Denmark . 
Italy 
Switzerland 

* Census Report, 1891, vol. iv. p. 61. 

t "Alien Immigration," Joiw. Statist. Soc, March, 1895. 



Average 


Proportion per 1000 


Emigration. 


of 


Population. 


18,836 




9-19 


247,279 




6-54 


30,709 




6-39 


18,901 




3-97 


8,344 




3-84 


102,466 




3-37 


8,007 




2-74 



14 



VITAL STATISTICS. 



Country. 


Average 


Proportion per 1000 


Emigration. 


of 


Population. 


Germany . 


123,985 




2-50 


Spain 


38,248 




2-18 


Hungary . 


17,717 




1-22 


Holland . 


5,107 




1-13 


Austria 


23,050 




0-96 


Belgium . 


4,371 




0-72 


Russia in Europe 


58,192 




0-63 


France 


10,429 




0-25 



From the point of view of the countries losing the above 
emigrants the proportion to the total population must be con- 
sidered, and from this standpoint Eussia's loss is a negligeable 
amount. From the point of view of the countries receiving the 
migration it is evident that the British, German, ItaKan, and 
Russian emigrations are of the very first importance. The most 
remarkable fact in the preceding table is that, "with the exception 
of the . United Kingdom, the countries sending out the largest 
numbers of emigrants are by no means always those in which the 
population is densest. Germany and Italy certainly stand high 
in the scale of density of population, but not so high as Holland 
and Belgium, yet the Dutch and Belgian emigration is both 
absolutely and relatively small. Norway and Sweden, on the 
other hand, combine an exceptionally heavy emigration with a 
scanty population, and in view of their rapid rate of natural 
increase may be said to be thinly peopled in consequence of this 
drain upon their resources. French emigration is so small as to 
exercise scarcely any appreciable effect, and Austrian emigration, 
though absolutely large, scarcely amounts to 1 per 1000 of the 
population." 



CHAPTEE II. 

POPULATION FPOM AN INTERNATIONAL STANDPOINT 

n^HE habitable globe is limited in area. The relative rate of 
JL natural growtli of the population of each country by excess 
of births over deaths has therefore a most important bearing on 
the final race characteristics of the population of the world. 

Fig. 3 shows the average birth-rate and death-rate of the 
different European countries for the five years 1891-95, while 
the distance between the two columns represents the natural 
increase in each country. The countries are arranged in the 
order of the magnitude of their annual natural increase, beginning 
with Prussia, in which it was 14*1, and ending with France, in 
which it averaged only "08 per 1000 of the population in the five 
years 1891-95> 

From the preceding figures it is easy to calculate in how many 
years the population of each country would take to double itself 
by natural increase. 

Here P' = PR", 

i.e., 2P=Pi?», 
.'.R" = 2. 

n log. R = log. 2, 
log. 2 lo2. 2 



In England?- =-0118, 

. log. 2 _ -301030 

■■"~loo-. 1-0118" -005093 



R log. (l-^?•)■ 

59-1 years. 



In Prussia the population would double itself by natural 
increase in 49-2 years; in England in 59-1 years; in Italy in 
65-7 years; in Austria in 74-1 years; and in France in 591 years. 

* In Fig. 3 the birth-rate of France should be 22-4, not 22-6 as given in 

the figure. 

15 



INTERNATIONAL STANDPOINT 



17 



These results of natural increase of population are disturbed by 
the effects of migration. It is therefore of interest to ascertain 
the net results as determined by all the factors at work, so far as 
they can be ascertained from historical records.* 

In 1789 the populations of the great European Powers were 
as follows : — 





Millions 


France .... 


. 26 


Great Britain and Ireland . 


. 12 


Russia .... 


. 25 


German Empire . 


. 28 


Of which Austria 


. 18 


Prussia 


5 



In 1815 the relative populations were as follows : — 

Millions. 
France . . . . . . . 29'5 

Great Britain and Ireland . . .19 

Austria ....... .30 

Prussia . . . . . . .10 

Russia ....... 45 

German Confederation (in which were in- 

chided jmrts of Austria and Prussia) . 30 

In 1890 the relative populations are stated by M. Bertillon to 
be as follows : — 

Millions. 
France 38-3 



Great Britain and Ireland 
Austro- H ungary 
German Empire 
Russia in Eurojie 
Italy .... 



38-1 
43-2 
49-4 
100-2 
30-5 



The most remarkable contrast shown in the preceding tables is 
between Great Britain and Ireland with a population of 12 
millions in 1789 and of 38 millions in 1890, and France with a 
population of 2G millions in 1789 and of only 38 millions in 
1890, not reckoning external colonies in either instance. 

Any conclusion from the above purely European figures would 
be erroneous which did not take into account the rapid growth of 
population in North and vSouth America, in Australia, and in 
Africa. In North America and in Australia, and to a less extent 
in South Africa, this rapidly increasing population is chiefly 
English-speaking. 



* Levasseuu, Annales de Dtmographic, 
Elements dc Demographic, 1896, p. 8. 

C 



1879, and J. Beutillox, 



18 VITAL STATISTICS. 

The increasing proportion borne by the population of the 
English self-governing colonies to that of the mother -country 
is shown in the following table arranged by Dr. Longstaff.* 
The population of the United Kingdom at each census being 
taken as 100, it will be seen that the united population of British 
North America and Australasia increased in 50 years from 7 to 21. 

Propoktion borne by Population of North American 
AND Australasian Colonies to that of the Mother-Country. 



Census. 


United Kingdom. 


Colon i 


1841 


100 


7 


1851 


100 


11 


1861 


100 


16 


1871 


100 


18 


1881 


100 


21 



The United States of America show the most gigantic increase 
of population of which we have records. In 110 years the 
population has become multiplied 21 times over. It would not 
be correct to say that the population has multiplied itself to this 
extent, as the greater part of the increase is due to immigration. 

Further particulars on the subject of this chapter are contained in 
Lo^gstayf's Studies in Statistics, 1891, pages 22-168. The population and 
chief vital statistics of the chief European countries are given on pages 
cviii.-cxxi. of the Fifty-Eighth Annual Report of the Registrar -General in 
England, or the corresponding parts of the annual reports for other years. 

The annual summary (page xxviii. of the report for 1896) and the 
corresponding quarterly reports and weekly returns of the Registrar-General 
give the population and chief vital statistics of 36 cities, of which 33 are 
foreign, European, American, Egyptian, and Indian cities. 



Studies in Statistics, 1891, p. 151. 



CHAPTER III. 

REGISTRATION OF BIRTHS AND DEATHS. 

"VTEXT to a correct enumeration of j^opulation the accurate 
l\ and complete registration of births, marriages, and deaths 
constitutes an essential basis of vital statistics. The question of 
registration of disease will be discussed in the next chapter. 

Twenty-three years ago Edmund Parkes stated the importance 
of statistics of births and deaths in the following words : " The 
attention now paid to public health is in a large degree owing to 
the careful collection of the statistics of births and deaths, and of 
the causes of death, made in England during the last forty years. 
It may truly be said, indeed, that not only all Europe, but 
gradually the entire world, has bee-n influenced by the work of 
the Registrar-General of England. We are now able to determine 
with some precision the limits of mortality and its causes, and are 
being led up to the consideration of the causes which bring about 
a high death-rate." 

History of Registration. The office of Registrar-General of 
England was created in IS3G, and civil registration began as the 
result of an Act of Parliament on July 1st, 1837. The first of 
the series of annual reports of the Registrar-General was puljlished 
in 1839, and to this first report Dr. W. Farr, who acted as "Com- 
piler of Abstracts" in the newly created General Register Office, 
contributed the first of that long series of letters, addressed to the 
Registrar-General, on the causes of death in England, with which is 
wrapped up our knowledge of the vital statistics of this country. 

Successive amendments to the law of registration were made, 
and in 1870 a new law was enacted rendering the registration of 
births and deaths compulsory. 

In the 39| years before registration became compulsory the 
registration of births was defective, the proportion of unregistered 
births being estimated at about 5 per cent. Only a small propor- 
tion of deaths were believed to have escaped registration, though in 
a considerable proportion the medical certificate of cause of death 
was either unsatisfactory or altogether wanting. The returns of 

19 



20 VITAL STATISTICS. 

1876 show the excellent effect of the compulsory law. The 
stated birth-rate of that year, 36 "6 per thousand, was the highest 
on record, being 1'2 per thousand higher than the average for 
the ten previous years ; while the number of uncertified deaths 
had greatly decreased. 

The Law as to the Registration of Births. The Act of 1836 
provides that the father or mother of a child, or in default of these 
the "occupier" of the house in which the child was born, or each 
person "present at the birth," or the persons "in charge of the 
child," must give notice to the registrar within 42 days of its 
birth, and sign the register in his presence. 

The medical practitioner in attendance at the birth may evi- 
dently, in exceptional instances, come within the scope of the 
above requirement. Similarly, if no notice has been given by any- 
one within the forty-two days, the registrar may, by notice in 
writing, require the medical man, or other persons present at the 
birth, to attend personally at his ofhce and give him the necessary 
information. The official instructions to registrars, however, enjoin 
upon them not to call upon persons present at the birth until they 
have failed to obtain the information from both the parents and 
the occupiers ; so that, in practice, medical men are seldom 
troubled in this matter. 

Registration of Births in relation to Vaccination. The 

Vaccination Act of 1867 makes it obligatory on the registrar at 
or Avithin seven days of the time when a birth is registered to 
give notice to the parent or other responsible person requiring the 
infant to be vaccinated within three months * of its birth, and 
stating particulars as to the hours of attendance at and place for 
public vaccination. 

By the Vaccination Act of 1871 every registrar must at least 
once a month transmit to each vaccination officer, whose district is 
wholly or partly comprised within his registration district, a true 
return of the births and deaths of infants under one year of age 
which have been registered since the last return was made. A 
fee of 2d. is payable for each entry. 

The Law as to Registration of Deaths.! 

"The law relating to the registration of deaths in England and 
Wales is mainly to be found in the Registration Act, 1836, as amended 

* The Vaccination Act, 1898, alters this period to six months, 
t The following particulars are taken chiefly from the Report of the Select 
Committee of the House of Commons on Death Certification, September, 1893. 



REGISTRATIOX OF BIRTHS AXI) DEATHS. 21 

by the Birtlis and Deaths Registration Act, 1874. Under Sections 10 
and 1 1 of the last-mentioned Act personal information of every death 
has to be given to the registrar of the district within live days of its 
occurrence l)y the nearest relatives of the deceased present at the 
death or in attendance during the last illness. In default of informa- 
tion of the death being given to the registrar by these persons, such 
information is to be given to him by the other persons mentioned in 
the section. Relatives present at the death or in attendance during 
the last illness who fail to comply with these provisions are liable to a 
penalty of 40s. 

" If the person required to give information of the death to the 
registrar send to him a written notice of its occurrence, accompanied 
by a medical certificate of its cause, the personal information recpxired 
to be given to the registrar need not be given within five days, but 
must be given within fourteen days (sec. 12, Act of 1874). 

" The law, however, does not require either notification or registra- 
tion as a condition precedent to burial or to disjjosal of the body. It 
is provided, that any person who buries or performs any funeral or 
religious service for the burial of any dead body as to which no 
coroner's oi'der for liurial or registrar's certificate of registration or 
of notification has been produced to him, shall, subject to a penalty 
of £10 in the event of default, give notice thereof in writing to 
the registrar within seven days. A like penalty is imposed by Section 
11 of the Burials Act, 1880 (as explained b}^ Section 2 of the Burials 
Act, 1881), upon the person having charge of or being responsible for 
a burial under that Act (sec. 17, ditto). 
" The registrar may register a death — 

(A.) On the statement of a 'qualified informant' attending 
personally for the purpose, and producing a medical certificate of 
the cause of death, when the deceased has been attended in the 
last illness by a registered medical practitioner. When there has 
been no such medical attendance the registi^ar must accej^t the 
' qualified informant's ' statement as to the cause of death. 

(B.) On the certificate of the finding of a coroner's jury, where 
an inquest has been held. 

" The registrar is empowered to issue a certificate to the effect that 
he has registered or received notice of a death, as the case may be, on 
production of which certificate burial can take place. 

"The certificate is to Ije issued gratuitously to the jjerson giving 
the information or sending the notice, or in the case of a burial under 
the Act of 1880 to the pei'son having charge of or being responsible 
for tlie burial (sec. 17, ditto). 

" The person receiving the certificate is bound, under a jienalty 
of 40s., to deliver it to the person who buries or jDerforms any funeral 
or religious service for the burial of the deceased (sec. 17, ditto). 

"(A.) Registration of the Cause of Death on the Statement of a 
Qualified Informant. — Where a person has been attended during his 



22 VITAL STATISTICS. 

last illness by a registered medical practitioner, it is the duty of the 
practitioner to give a certificate stating the cause of death to the best 
of his knowledge and belief. If he fails to give a certificate he is 
liable to a penalty of 40s., and if he gives a false certificate he is liable, 
on summary conviction, to a fine of £10, or on indictment to seven 
years' imprisonment. He may, however, refuse to give a certificate on 
reasonable grounds (sec 20, ditto). 

"The certificate is to be given by the medical man to the person 
required under the Registration Act to give information concerning 
the death, called the ' qualified informant,' whose duty it is to deliver 
it to the registrar under a penalty of 40s. (sec. 20, ditto). 

" (B.) Registration on the Certificate of the finding of a Coroner's 
Jury. — A death may be registered upon the certificate of the coroner, 
who is bound, after the termination of an inquest on any death, 
to send to the registrar such certificate of the finding of the jury 
within five days, the jury being bound to inquire of and to find 
the particulars for the time being required by the Registration Acts to 
be registered concerning the death. Where an inquest has been held 
a medical certificate of the cause of death need not be given to the 
registrar, but the certificate of the finding of the jury furnished by 
the coroner is sufficient, and the registrar is bound to take the finding 
of the jury in the words of the coroner, and this finding supersedes 
any previous certification of the cause of death. The coroner may 
order burial before registry of the death, but only after inquest, and 
unless an inquest is held there is no power to register a death upon 
the coroner's certificate (sec. 45, ditto). 

" If a registrar becomes aware of a death that has not been regis- 
tered in accordance with the ordinary regulations in that behalf, he 
may, at any time after the expiration of fourteen days, and within 
twelve months from the day of such death, call upon the person upon 
whom the registration of the death would have devolved to attend 
before him at a specified time, for the purpose of giving information 
as to such death (sec. 13, ditto). 

"After the lapse of twelve months a death can only be registered 
upon the authority of the Registrar-General (sec. 15, ditto)." 

ISTo fee is payable by the informant when a birth or death is 
registered, unless the registrar is required, in pursuance of a 
Avritten requisition, to attend the private house in which the birth 
or death has occurred, in which case the informant must pay a fee 
of one shilling. 

Eelation of Eegistrar to Medical Officer of Health. Ey sec. 
28 of the Births and Deaths Eegistration Act, 1874, each urban 
or rural Sanitary Authority can require the Eegistrar of Births 
and Deaths to supply returns of the births and deaths within his 



REGISTRATION OF RIRTIIS AND DEATHS. 23 

district. These returns are usually made weekly, but au imme- 
diate return can be required of deaths from infectious diseases. A 
fee of '2d. for each return and for each entry of deaths is payable 
by the Sanitary Authority. The medical officer of health can 
re(juire a complete copy of the entry in the register, including the 
occui)ation of the deceased, as well as the particulars in the official 
form of certificate given on page 31. 

Still-Births. No record of still-born children may be made in 
a register of births or deaths. Even when an inquest has been 
held, and when, according to the finding of the jury, there was 
not sufficient evidence that the chikl was born alive {i.e., that it 
lived after complete sejjaration from the Iwdy of its mother) no 
record may be made. But if a child be born alive, no matter how 
soon it may die, both the birth and the death must be registered. 

Under section 18 of the I5irths and Deaths Registration Act of 
1874 a penalty of £10 is imposed upon any person who buries the 
body of a deceased child as if it were still-born, and a like penalty 
is imposed upon any person who has control over a burial-ground, 
and who permits the body of a deceased child to be buried in such 
burial-ground as if it were still-born, or who buries or permits to 
be buried in such burial-ground any still-born child without a 
written certificate from a medical practitioner that such child was 
not born alive, or a declaration from a qualified informant or a 
coroner's order, if there has been an inquest. 

The Report of the Committee of the House of Commons on 
Death Certification (p. 22) says : "There is reason to think that if 
the statistics on the subject could be ol)tained, it would be found 
that the number of children buried in the United Kingdom 
annually as still-born is enormous " ; and the , Committee are 
further convinced that " the absence of legal requirement that 
such births should be registered prior to disposal of the bodies is 
fraught with very serious danger to child-life." This is especially 
so in the case of illegitimate children. 

There being no trustworthy English figures on the subject, the 
following from tlie official returns of Ilamburg are of interest. 
During the years 1882-96 inclusive the proportion of still-born to 
total births varied from 2-91 to 3-67 per cent. The proportion 
among boys varied from 2 89 to 4-24 per cent. ; amcmg girls from 
2-91 to 3-58 per cent. The proportion among infants born in 
matrimony varied from 2-79 to 340; among illegitimate infants 
from 4-47 to G-40 per cent. In the same returns still-births 



24 Vital statistics. 

are classified according to whether they were premature, and 
whether the death occurred during or before parturition. 

Uncertified Deaths. The absence of a medical certificate of 
cause of death does not necessarily involve a report to the coroner 
by the registrar. He must report the death to the coroner " where 
it appears that the death was caused directly or indirectly by 
violence, or was attended by suspicious circumstances, and when- 
ever the death is stated to have been sudden, or the cause of death 
is stated to be 'unknown.'" This applies to all cases, whether 
certified by a registered practitioner or not. In other cases the 
registrar may accept the statement of the informant as to the 
cause of the death, and the information thus accepted may in- 
clude a certificate from an unregistered practitioner. 

The registrar must report to the coroner the death of every 
infant which dies in a house registered under the Infant Life 
Protection Act, 1872. It is the duty of the local authority to 
furnish soon after the 1st January in each year a complete list 
of all such registered houses, and to notify from time to time any 
alteration therein. If the local authority omits to furnish these 
lists it is the registrar's duty to apply for them. 

In 1895 the causes of 91'68 per cent, of the total deaths in 
England and Wales were certified by registered medical practi- 
tioners, and the causes of 6 "00 per cent, by coroners after inquest, 
while the causes of the remaining 2 '32 per cent, of the total 
deaths were not certified. The 13,173 uncertified cases included 
the deaths of infants who had been attended only by midwives, 
and those of persons who had been attended by unregistered 
practitioners, as well as those of persons who had received no 
"medical" attendance of any kind. In registration counties the 
proportions per cent, of unregistered deaths ranged from 0-71 in 
London and 0'88 in Wiltshire to 4'58 in Huntingdonshire, 4"78 in 
IS'orth Wales, and 5'88 in Herefordshire.* In the same year just 
one-third of the uncertified deaths were of infants under three 
months of age, and these deaths were 6 "2 7 per cent., or about one 
in sixteen of all the deaths under three months of age. The 
proportion of uncertified deaths fell abruptly to 2 '49 per cent, 
between three and twelve months of age ; the minimum, 0"85 per 
cent., being reached at fifteen to thirty-five years of age, after 
which it gradually rose with advancing age. 

* Fifty -Eighth Annual Report of the Registrar-General. 



RE(USTRATION OF BIRTHS AND DEATHS. 25 

Inquests. When an inquest is held on any dead body it is the 
duty of the coroner to send a certificate to the registrar within 
five days after the finding of the jury is given, giving full particu- 
lars as to this finding. The only person upon whom the duty 
devolves of deciding wlusther cases are suspicious in any case, 
and if so, of referring them to the coroner, is the registrar. It 
seems veiy desirable tliat this option should l)e removetl from him 
and transferred to the coroner. In a considerable i)roportion of 
luicertified deaths that are sul)mitted by the registrars to the 
coroner the latter decides in an informal manner that no inquest 
was required after an investigation made by his officer, who 
frequently is a parish beadle or })olice officer. Such a procedure 
would be justifiable if a private medical investigation were 
instituted, but as matters now stand there is little reason to 
doubt that crimes occasionally remain undetected, which skilled 
investigation would have In'ought to light. Even when a coroner's 
inquest is held tlie result may be little more satisfactory, the 
inquiry being often perfunctory and its result dubious, owing, 
among other causes, to the fact that autopsies have not infrequently 
been omitted. 

The death on account of which an inquest is held is very 
commonly registered subsequently as "from natural causes," the 
coroner considering his sole function to be the detection of crime, 
and ignoring entirely the medical problems toward the solution of 
which he might contribute. In other inquest cases the certification 
is almost equally defective, the cause of death being returned as 
"sudden death," "death by the visitation of God," "found dead," 
etc. Such returns are useless for classification. No coroner's 
inquest is satisfactory which does not include a post-mortem 
examination liy a competent medical practitioner. 

Recommendations of Committee of House of Commons on 
Death-Certification (1893). The Committee give the following 
summary of their reconunendations : — 

" (1.) Tliat in no case should a death be registered without production 
of a ceitificate of the cause of death signed l)y a registered medical 
jiractitioiier or by a coroner after inquest, or in Scotland by a Pro- 
curator Fiscal. 

"(2.) That in each sanitary district a registered medical practitioner 
should lie appointed as public medical certifier of the cause of death 
in cases in which a certificate from a medical jjractitioner in attendance 
is not fortlicoming. 

"(3.) That a medical practitioner in attendance should l)e I'L-quired, 



26 VITAL STATISTICS. 

before giving a certificate of death, to personally insjject the body, but 
if, on the ground of distance or for other sufficient reason, he is unable 
to make this inspection himself he should obtain and attach to the 
certificate of the cause of death a certificate signed by two persons, 
neighbours of the deceased, verifying the fact of death. 

" (4.) That medical ^practitioners should be required to send certifi- 
cates of death to the registrar, instead of handing them to the repre- 
sentatives of the deceased. 

" (5.) That a form of certificate of death should be prescribed, and 
that in giving a certificate medical practitioners should be required to 
use such form. 

" (6.) That it should be made a penal offence to bury or otherwise 
dispose of a body, except in time of epidemic, without an order from 
the registrar stating the place and mode of disposal, which order, after 
it has been acted upon, should be returned to the registrar who 
issued it. 

"(7.) That it should be made an offence to retain a dead body 
unburied or otherwise legally disposed of beyond a period not exceed- 
ing eight daj^s, except by permission of a magistrate. 

"(8.) That the practice of burial in pits or common graves should 
be discontinued. 

"(9.) That still-births which have reached the stage of develop- 
ment of seven months should be registered upon the certificate of a 
registered medical practitioner, and that it should not be permitted 
to bury or otherwise dispose of the still-birth until an order for burial 
has been issued by the registrar. 

"(10.) That, subject always to the discretion of the Crown Office, 
the result of precognitions taken by the Procurators Fiscal in Scotland 
or the precognitions themselves should be communicated to the repre- 
sentatives of the deceased when application is made for the same." 

Improvements in Kegistration required. The preceding sketch 
of the system of registration now in force renders a detailed 
discussion of the defects of registration unnecessary. The recom- 
mendations of the Parliamentary Committee embody some of the 
more important improvements required. These do not include 
the appointment of medical chief registrars, though this is referred 
to favourably in their report. This reform would probably do 
more than anything else to improve our system of registration. 
As matters now stand, when there is no medical certificate of the 
cause of death, the registrar makes inquiries of the relatives of 
the deceased person, and if he is satisfied with their explanation 
of the cause of death, and has satisfied himself that there are no 
suspicious circumstances connected with the death, enters it 
according to their statements, adding that the death is "not 
medically certified." 



REGISTRATION OF BIRTHS AND DEATHS. 27 

Such a S3''stem is obviously open to the grossest abuse. All 
this would be remedied if, as Dr. Farr proiiosod in 1864, medical 
retjisfrars were appointed, who should preferably be the medical 
officer of health of the district. It should 1)e part of his duty to 
make a medical inquisition into the cause of death in all dubious 
cases. In Ireland medical men hold the position of registrars, 
and the evidence of Dr. Grimshaw, the Registrar-General of 
Ireland, appears to show that the causes of death are more 
correctly certified in Ireland than in other parts of the United 
Kingdom. 

Use made of Information furnished by Registration. Weekly 
and quai'terly returns are made liy the local registrars to the 
Registrar-General, Somerset House, London. These are collated 
and abstracted ; and from these al)stracts the periodical reports 
issued from the General Register Otlice are prepared. The follow- 
ing arc the chief of these reports : — 

1. A Weekly Return of the births and deaths from all causes, 
and from the chief infectious diseases, in each of thirty-three great 
English towns, with similar particulars for the registration sub- 
districts of London, and meteorological and other data for the 
week. The Weekly Return also embodies important returns from a 
number of foreign cities. 

2. A Quarterly Return of marriages, births, and deaths regis- 
tered in the divisions, counties, and districts of England, with 
certain detailed information relating to the deaths in each regis- 
tration sub-district. 

3. An Annual Summary of the births, deaths, and causes of 
death in London, in the thirty-three great towns, and in sixty-seven 
other large towns, with an appendix on the metropolitan water- 
supply. 

4. An Annual Report of births, deaths, and marriages in 
England, containing fuller particulars than the preceding reports, 
but dealing in detail with registration districts and sub-districts, 
not with towns, unless they happen to coincide with these. 

5. A Decennial Supplement, containing i7iter alia life-tables 
representing the experience of England and of its healthy dis- 
tricts, and an important discussion of occupation in relation to 
mortality. These supplements contain some of the most im- 
portant work of the General Register Office, and are invaluable 
for reference. The last one (for 1881-90), by Dr. Tatham, is 
indispensable to vital statisticians, and a worthy successor of the 



28 VITAL STATISTICS. 

earlier supplements by Drs. Farr and Ogle, which are classical 
contributions to the subject. 

The student should make himself familiar with each of the 
above reports, as well as with the last General Census Report. It 
is only by this means that he can make full use of the mine of 
information that they contain. Although to some extent the 
different reports overlap, they are all necessary for the develop- 
ment of the full value of the vital statistics of England. 

The weekly reports are issued on the Tuesday morning next 
f olloAving the end of the week to which they refer ; the quarterly 
reports in the month following the end of the quarter ; while the 
annual reports usually appear toward the end of the year subse- 
quent to the year to which they apply. The annual summary, 
however, appears in April or May. In regard to the delay in the 
issue of the annual reports. Dr. Farr says : " They may be re- 
garded as storehouses of facts, which have been arranged on 
methods that are approved as the most useful and convenient, 
and to which, both noAV and in future years, students of vital 
statistics may resort for the elucidation of questions bearing on 
the social condition of the people, on national progress, on life, 
health, and disease. It is important they should be done well. It 
is desirable only in the next degree that they should be done 
quickly." 

The value of these various reports can scarcely be exaggerated. 
The rates of mortality in the Aveekly reports require, hoAvever, to 
be accepted with caution, as large fluctuations in short periods may 
be due to accidental causes. But in indicating the character and 
amount of prevalent diseases, and their geographical distribution, 
they are invaluable. As Farr eloquently puts it : " Thus observers, 
like watchmen on the walls, are ever on the look out, so that they 
can see exactly what is going on, and neither plague, cholera, nor 
any other great epidemic can take the nations by surprise. The 
deaths serve the purpose of a self-registering inspection. Death 
cannot be deceived by sham defences." 

The regulations as to registration of deaths and burials in England may 
be contrasted with those in other countries by reference to Palmberg and 
Newsholme's Treatise on Public Health — England, p. 11 ; Brussels, p. 230 
(system of verification of deaths) ; Paris, p. 279 ; Berlin, p. 377 ; Vienna, 
p. 418 ; Sweden, p. 441. 

The Report of the Select Committee of the House of Commons on Death 
Certification also embodies some valuable international information, as well 
as fuller details on the whole subject, than can be given here. 



CHAPTEE IV. 

DEATH CERTIFICATION AND CLASSIFICATION OF 
CAUSES OF DEATH. 

rpHE Registration of Causes of Death has given an immense 
X impetus to sanitary work, and it is scarcely too much to say 
that modern sanitary science owes its existence to the registration 
of deaths and their causes, and tlie locahsation of insanitary 
conditions thereby insured. By its means, conjoined with the 
census returns, we are able to submit to numerical analysis the 
facts relating to the laws of vitality, the influence of age and 
sex, of civilization, occupation, locaHty, season, and many other 
agencies ; and our knowledge of all the facts bearing on health 
and disease has attained a precision never before known. 

There are certain fallacies in the registration of causes of 
death, partly owing to the imperfection of medical science and 
of a portion of its practitioners, and partly owing to differences 
of nomenclature and classification of diseases. 

The deaths uncertified have been already considered. It is 
evident that as these gradually diminish there will be a trans- 
ference to death under some definite head. The same applies 
to the mortality from ill-defined causes, the increased accuracy of 
diagnosis causing a steady decrease under this head. Thus in 
1895 there were in England 25,762 deaths classed as from '■^ill- 
defined and not specified cmises," being 4"5 per cent, of the total 
deaths. In 1862 the death-rate in England and Wales per million 
living was 2104 under this head; in 1872 it was 1854; and in 
1882 it was 1154, decreasing still further to 849 per million living 
in 1895. 

The number in 1895 would have been greater had not 5255 
answers been received to letters of inquiry concerning doubtful 
cases previously sent out from the Registrar-General's office (a 
system first started in 1881, when about 1200 letters of inquiry 

29 



30 VITAL STATISTICS. 

were sent to medical men, asking for further information than 
was given in their certificates.) * 

Faulty diagnosis and the desire to shield relatives are perhaps 
the most prolific sources of inaccurate and indefinite certificates. 
In many cases the certified causes of death, e.g. cardiac syncope, 
as Dr. Eumsey long ago pointed out, are nothing more than modes 
of death. The most common headings found in this indefinite 
class are abdominal disease, debility, atro^nhy, inanition, innuti'ition, 
toasting, congenital debility, cachexia, tumoiir, blood-poisoning, 
Ticemorrliage, drojjsy, convulsions, etc. 

Peritonitis standing alone is similarly unsatisfactory without its 
cause being defined, a large proportion of the cases being puerperal 
in origin. 

In many parts of the country, especially in Wales, the causes 
of death stated by friends are very commonly accepted by the 
local registrar without any medical certificate. This probably 
explains in part the prevalence of consumption in Wales ; any 
wasting disease, especially if accompanied by cough, being called 
by that name. 

The mortality from " abdominal disease " is on the decrease, 
which accounts for a part of the registered increase in mortality 
from cancer in recent years. 

The lack of uniformity of nomenclature among medical men 
is another source of fallacy. There appears to be a fashion even 
in the names of diseases. In one doctor's practice nearly all the 
deaths from respiratory diseases will be returned as bronchitis or 
congestion of the lungs, in another perhaps as pneumonia. It is 
necessary, therefore, in instituting comparisons for a series of 
years, to take preferably a Avell-marked and easily recognizable 
cause of death, or where this is impracticable, a large group of 
diseases in which the sources of fallacy tend to counterbalance 
each other. 

In dealing Avith such causes of death as alcoholism, syphilis, 
and insanity, serious sources of statistical error arise ; and the 
same remark applies to a variable extent to diseases affected by 
improvement in diagnosis and the still greater improvement in 
accuracy of certification, such as renal diseases, internal cancer, etc. 

The official form of death certificate and the official suggestions 
to medical practitioners are here appended, and it is most desirable 
that the suggestions should be rigidly folloAved. 

* For particulars as to the results of these inquu'ies see p. 18, Eegistrar- 
GeneraVs Annual Report, 1895. 



DEATH CERTIFICATION. 



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32 VITAL STATISTICS. 

Suggestions to Medical Practitioners respecting 

1. State the Causes of Death in terms as precise and brief as possible, and 
use the names adopted in the nomenclature of the Royal College of Physicians, 
taking the English names in preference to the Latin or other foreign equiva- 
lents. Vague terms such as Decline, Tabes, Cachexia, cfcc, should be avoided. 
So also Hcemorrhaga should not be assigned as a Cause of Death without 
further specification of its probable origin and the organ affected. Tetanus 
again should be defined as Idiopathic or Traumatic, and if the latter the 
cause and nature of the injury should be added. 

2. "Write the Causes of Death, when there are more than one, under each 
other, in the order of their appearance, and not in the presumed order of 
their importance. 

3. Medical Practitioners should not content themselves with assigning, as 
is too often done, some prominent symptom as the Cause of Death ; but 
should state, whenever possible, the disease to vhich the symptom was due. 
Sometimes, doubtless, it will happen that the nature of the fatal disease 
cannot be ascertained with certainty ; in such cases, and in such alone, a 
leading symptom should be assigned as the Cause of Death. " Dropsy " 
should not be returned as the Cause of Death without stating whether the 
Dropsy loas due to Heart Disease, or Renal Disease, or the like ; when 
"Dropsy" alone is returned, it is assumed that the cause of this symptom 
was not ascertained. 

Similarly, when the immediate Cause of Death was dependent upon some 
general condition, such, for instance, as the Strumous, the Syphilitic, or the 
Rickety constitution, this remoter Cause should be stated, as well as the more 
immediate Cause. 

4. In certifying Deaths from any form of Continued Fever, state the kind 
of Fever, and, in so doing, be especially careful to adopt the nomenclature of 
the College of Physicians. Avoid all such ambiguous terms as Low Fever, 
Miliary Fever, Brain Fever, Hectic Fever, Febrile Attack, &c. Similarly 
avoid the term " Typhoid Pneumonia," which may mean either Asthenic 
Pneumonia with typhoid symptoms, or Enteric Fever Avith secondary 
Pneumonia. 

Do not use the term Infantile Remittent Fever for Enteric Fever in 
children. 

5. "When the Cause of Death has been verified by a, post-mortem examina- 
tion, the letters P.M. should be added. 

6. State, in fatal cases of Small-pox, whether "Vaccination had been 
performed with effect and when, or whether the deceased was unvaecinated. 
If possible, state the evidence of "Vaccination, e.g., "two bad marks." The 
term "Vaccinated" sliould be used in preference to "After Vaccination." 
" Small-pox after Vaccination, 21 days," is ambiguous, because the question 
arises whether the period (21 days) refers to the Small-pox or to the 
Vaccination ; the Cause of Death .should be certified as "Small-pox 21 days 
(vaccinated)." 

7. Whenever Child-birth has occurred uithin one month before death, this 

N.B.— No Medical Practitioner is justified in giving a Certificate unless 
* The above are the official suggestions prefacing the book of blank death- 



CLASSIFICATION OF CAUSES OF DEATH. 33 

Certificates of the Cause of Death. ^' 

fact should invariably be certified, even though it may be believed that the 
Child-birth had no connection with the Cause of Death. 

8. The Duration of primary and secondary diseases in these Certificates 
will always be considered to mean the time intervening between the first 
apjiearauce of well-marked characteristic symptoms and death. 

Small-pox, Scarlet Fever, Measles, and other similar febrile diseases 
should, however, be dated from the rigors and first symptoms ; not from the 
later appearance of the eruption. 

Ague, Efjilepsy, Angina Pectoris, and other maladies that occur in fits or 
jiaro.xysms, should he dated from the first attack, the duration of the last lit 
being added. 

The duration should be stated in minutes or hours when the disease 
is fatal in less than 48 hours ; in days when the disease is of less than 
50 days' duration ; in months or years when the disease is of still longer 
duration. 

Examples: — (a) Scarlet Fever .... 30 days 
Anasarca ..... 7 days 

Implies that the earliest symptoms of Scarlet Fever occurred 30 days before 
death, and that Anasarca was first noticed 7 days before death. 

(b) Epilepsy ..... 5 years 
Last Fit ..... 6 liours 

Implies that the first Epileptic fit occurred five years back, and that the 
fatal fit lasted 6 hours. 

(c) E.xcessive use of Spirits . . 

Delirium Tremens ... 6 days 

Implies that the deceased had been for an unknown time given to intemper- 
ance, and suffered from Delirium Tremens for 6 days before death. 

9. SURGEONS in all cases of operation should return (a) the jirimary 
disease or injury ; (b) the kind of operation ; (c) the secondary diseases — 
such as Erysipelas, Purulent De[)Osits, &c., and should state also the time 
from commencement of the primary disease, the time from the operation, 
and the time from the appearance of secondary disease, i-cckoniwj in each 
instance to the death. 

Examples : — 

Femoral Hernia .... 3 years 

Strangulated ..... 5 days 

Operation ...... 2 days 

Peritonitis ..... 45 hours 

10. In every case of Death from violence, or susjiectod violence, the 
Medical Practitioner should advise the friends of the deceased to jjring the 
case to the knowledge of the Coroner in order that he may decide as to 
holding or not holding an Inquest, inasmuch as the Coroner may otherwise 
feel it his duty, when the case comes to his knowledge, to order the body to 
be e.xhumed and inquiry instituted, 

HE WAS PERSONALLY IN ATTENDANCE UPON THE DECEASED DURING THE LAST ILLNESS. 

certilicatej), obtainuble by any qualilicd practitioner Iruni tliB rogistrar. 
D 



34 VITAL STATISTICS. 

Nomenclature of Diseases. The necessity of uniformity is 
obvious, as otherwise any classified results must be untrustworthy. 
The nomenclature of the Royal College of Physicians of London, 
of Avhich the third edition, being the second revision, appeared in 
1896, is the standard adopted in all English-speaking countries, 
and all death returns should be made in accordance with this. Of 
course no classification Avill obviate the differences due to the 
opinions of individual practitioners, as, for instance, the return by 
one practitioner of death as due to croup which another would 
certify as diphtheria. [See Postscript, p. 346.] 

The preface to the first edition of the Royal College_ of Physi- 
cians' classification contains many weighty remarks bearing on this 
question of Nomenclature and Classification, which are here 
summarised. It is pointed out that the great ends of such a 
nomenclature are (1) to perfect the statistical registration of 
diseases, (2) to form a steady basis on Avhich medical experience 
can be built up, and (3) to thro^v light on the causes of disease, 
which, in many cases, may thus be brought within the range of 
preventibility. 

The committee appointed by the Royal College of Physicians 
expressed their sense of the desirability of as little deviation as 
l}0ssible from the list of names employed by the Registrar-General 
of England ; as otherwise his settled plans and his forms of returns 
Avould require to be remodelled, the comparison of future wdth past 
returns Avould be made difficult and perplexing, if not_ impossible, 
and a damaging break would be caused in evidence which becomes 
more and more trustworthy and valuable in proportion as it is 
prolonged and continuous. 

They also refused to exclude names, such as dropsy, palsy, con- 
vulsions, merely because they may seem to express only vague or 
imperfect knowledge, agreeing with Dr. Parr that the refusal to 
sanction such terms as these in the region of disease " would have 
an obvious tendency to encourage reckless conjecture " in making 
returns. The Revision Committee (1885), however, while fully 
acknowledging the wisdom of the above remark, "felt it right to 
indicate as strongly as possible the necessity of avoiding the use of 
the names of symptoms wherever the names of diseases or of 
causes of symptoms could Avith reasonable certainty be substituted." 
Thus the term apoplexy should only be used when the morbid 
condition causing it cannot be recognized. 

The classification of diseases is a more difficult task than their 
nomenclature, and it is pointed out that the comparison of single 



CLASSIFICATION OF CAUSES OF DEATH. 35 

diseases {if well marJced) is more reliable than that of groups of 
diseases. But although a good classification is very difficult, it is 
very important, as it "aids and simplifies the registration of 
diseases, helps towards a more easy comparison and knowledge of 
them, and towards the storing of experience respecting them, and 
facilitates the discovering of general principles from the collected, 
grouped, and compared phenomena." 

^ A classification might be according to (1) symptoms, (2) causes, 
(3) intimate nature, (4) tissues or systems of the body affected, 
(5) parts of the body as they lie anatomically. The committee 
based their classification on anatomical considerations, and in 
subservience to this grouped diseases as General and Local. 
General diseases were divided into section A, comprehendinn- 
those disorders which appear to involve a morbid condition of the 
blood, such as the specific fevers; and section B, comprising for 
the most part disorders which are apt to invade different parts of ' 
the same^ body simultaneously or successively, sometimes called 
Constitutional Diseases. The Eevision Committee, in the second 
edition, pointed out that the name General Diseases fails to express 
the nature of the group which it heads, and that Morbi Corporis 
Universi would convey more clearly the idea intended, or "Diseases 
of the whole body and diseases which may be distributed in several 
parts at one time,— General Diseases." In the third edition the 
term " General Diseases " is restored, and is used to include not 
only diseases properly so called, but morbid conditions affecting 
either the whole body or more than one part. 

The system of classification of diseases must vary according to 
the object of the registration. Thus (1) the Eegistrar-General 
tabulates deaths and the causes of death. His is essentially a 
classification based on an etiological basis, and thus possesses a 
supreme importance from a hygienic standpoint. The College of 
Physicians' classification is one of diseases, while that of the 
Eegistrar-General is of assigned causes of death; one is patho- 
logical, the other etiological. This is seen very strikingly in the 
classification of injuries, the College of Physicians classifying them 
according to their position and nature, while the Eegistrar-General 
divides them into accidental, homicidal, suicidal, and execution.* 

(2) The army and navy medical departments tabulate diseases 

Similarly oases of whooiiiiig-cough with death from pneumonia are 
referred by the Registrar-General to the former and niucli more remote cause 
of death. Most classitications which give a single cause of death in their 
ultimate analysis would ascribe tlie deatli to i»neumonia. 



36 VITAL STATISTICS. 

as well as deaths occurring in the two services. Hence many 
diseases appear Avhich are not seen in the death returns. 

(3) The registrars of hospitals and the medical ofificers of 
infirmaries deal mainly in their returns with the distribution of 
morbid processes within the body, and seek rather to find the 
proportion of deaths to attacks than the proportion of number of 
attacks or deaths to population. As this method takes note of 
ultimate and proximate causes of deaths, stating the original 
disease and its complications, there is commonly for each individual 
disease a multiple return. 

It is evident, therefore, that there must co-exist two dissimilar 
methods of classification, of Avliich the etiological is for our present 
purposes by far the most important. 

We must repeat that the knowledge of a Avell-marked single 
disease is safer for comparative purposes than that of a group of 
diseases. For instance, the term Zymotic Diseases includes enteric 
fever and whooping-cough, which have a very unequal value as a 
test of the sanitary condition of any locality. In regard to 
constitutional diseases, it should be remembered also that certain 
diseases, such as contracted granular kidney, which are classed 
under local diseases, might perhaps more justly come under the head 
of constitutional diseases, while in other instances the converse 
holds good. 

The Eegistrar-General's classification can be seen by reference 
to his annual reports, e.g., report for 1895, p. 52 et seq. This 
classification is employed almost solely in the annual reports of 
medical officers of health. A glance down the list of diseases 
shows that in certain minor particulars it is not abreast with 
medical knowledge. Thus tubercular diseases, and almost cer- 
tainly rheumatic fever, should be transferred from constitutional 
to infective diseases, and tetanus to the same group from diseases 
of the nervous system. Fatal croup again in the vast majority of 
cases means diphtheria, and probably the same remark applies 
to quinsy. These two diseases Avere formerly placed by the 
Registrar-General next to diphtheria, and were relegated to their 
present position among diseases of the respiratory and digestive 
system respectively, in deference to the classification of the Royal 
College of Physicians. 

For illustrations of statistical tables useful in the compilation of the annual 
report of a medical officer of health, see Palmberg and Newsholme's Treatise 
on Public Health and its Applications in Different European Countries, p. 12 
et seq. 



CHAPTEE V. 

REGISTRATION OF SICKNESS. 

rpHE registration of deaths gives a very imperfect view of the 
X prevalence of disease. The medical officer of health would 
have a greatly increased power of protecting the public health if 
he could by early information of every case of preventible 
disease track its development and progress, and adopt measures 
of prevention. Dr. Lyon Playfair in 1874 emphasized the 
importance of registration of sickness in these Avords : " The 
record of deaths only registers, as it were, the wreclcs which 
strew the shore, but it gives no account of the vessels which were 
tossed in the billows of sickness, strained and maimed as they 
often are by the eflects of recurrent storms. Registration of 
sickness would tell us of the coming storms, and enable us to 
trim our vessels to meet them." 

Mortality statistics necessarily "ignore all that precedes the 
close of life." The prevalence of a given disease cannot be 
gauged with absolute accuracy in the absence of registration of 
each case of the disease, except when, as in hydrophobia, the 
disease is always fatal. 

It is fallacious to assume any fixed ratio between sickness and 
mortality. The fatality of a given infectious disease varies (jreatly 
in different outbreaks under varying circumstances. The highest 
ratio of sickness is occasionally found associated with a favourable 
rate of mortality. Cholera is much less fatal towards the end of 
an epidemic than at its beginning ; so a conclusion drawn simply 
from the death returns might easily exaggerate the diminution in 
the prevalence of the disease. There are some diseases, again, 
the knowledge of which is desirable, but which do not perceptibly 
affect the mortality (except in some cases, through secondary con- 
sequences), as quinsy, mumps, chicken-pox, gonorrhoea. 

The medical officer of health, who only knows of fatal cases of 
preventible diseases, is to a large extent in the impotent position 

37 



38 VITAL STATISTICS. 

of a mere recorder of events. If he knew of ev&'y case, pre- 
ventive measures could be adopted at an early stage, and the 
outbreak could be tracked to its true origin, as not a single link 
in the chain of evidence would be missing. 

Death returns are silent about the large mass of common 
sickness, which, although it may disable a man, is not " unto 
death." From an economical point of view this sichness is more 
imjyortant than deatlis, "for it is the amount and duration of 
sickness rather than the mortality that tell on the prosperity 
of a community." (Dr. Dickson.) Or as Charles Dickens has 
stated it : "It concerns a man more to know his risks of the fifty 
illnesses that may throw him on his back than the possible date 
of the one death that must come. We must have a list of killed 
and of tJie 'wounded too ! " 

Local returns of disabling sickness of every description would 
not only enable us to deal jiromptly with epidemic disease, but 
would also throw great light on the influence of season and 
climate, of social condition, and of trades and manufactures on 
health, and would thus enable preventive measures of diverse 
kinds to be brought into action. 

It is evident that even Avere it possible it is not requisite to 
knoAv of every case of sickness. The lines of demarcation 
between health and sickness are ill-defined, and it would be 
necessary to limit the returns to disabling sickness. 

Attempts made to Register Sickness. We cannot attempt 
here to give a history of the various attempts made in this 
country to obtain registration of prevalent diseases by B. W. 
Richardson, Rumsey, and others. Two organized efforts which 
were for some time successful may be briefly mentioned.* 

The first Avas made by the Metropolitan Association of Health 
Oflicers in 1857, and included sickness of all kinds attended at 
the public expense, in hospitals, and by poor law medical officers, 
dispensaries, workhouses, etc. The returns were contributed 
gratuitously by the respective medical officers, the general Board 
of Health undertaking to print and circulate the weekly and 
quarterly tables. Of 109 hospitals and dispensaries generally less 
than 50 contributed ; in some cases boards of guardians refused 

* For fuller particulars of the history of notification of sickness see 
a paper by the author on "A National System of Notification and Regis- 
tration of Sickness," Jour. Statist. Sue, vol. lix. part i., 1896. 



REGISTRATION OF SICKNESS. 39 

to supply information ; and before the expiration of the second 
year tlie tables, which had never been complete for all sickness 
attended at the pul)lic expense, ceased to appear, voluntary 
co-operation being evidently unecpial to the enterprise. It should 
be noted also tliat the returns were not entirely trustworthy so 
far as they Avent, for the diseases and accidents notified were not 
all new cases ; that many returns represented patients who liad 
come up from country districts for hospital treatment ; and that 
an indefinite numl)er of patients, who wander from hospital to 
hosi)ital, must have been notified more than once. Dr. Ransome 
and the Sanitary Association of Manchester and Salford organized 
in 18G0 a system of registration of sickness for these towns 
which appears to have been very complete and exact, and was 
not finally abandoned until the compulsory notification of in- 
fectious diseases came into force nearly twenty-five years later. 
An attempt was made, at Dr. Ransome's suggestion, to obtain 
simultaneously Avith the returns of disease a record of the 
mortality occurring amongst the cases reported. This was then 
compared Avith the total mortality, and a very fair guess could 
thus be made as to the total number of cases occurring within the 
district. 

The Eequirements of a Plan for the registration of disease 
have Ijeen set forth by Dr. Farr as follows, in the supplement to 
the Registrar-General's Thirty-fifth Annual Report: "The reports 
of the existing medical officers are of great practical value, and 
will become more valuable every day. What is wanted is a staff 
officer in every county or great city, with clerks to enable him to 
analyse and publish tlie results of weekly returns of sickness to 
be procured from every district ; distinguishing, as the army 
returns do, the new cases, the recoveries, the deaths reported 
weekly, and the patients remaining in the several hospitals, 
dispensaries, and workhouses. These compiled on a uniform 
plan, when consolidated in the metropolis, would be of national 
concern. It has been suggested that the returns of sickiiess 
should, to save time, be sent to London, and there analysed on 
a uniform system as the causes of death are. That with the 
present postal arrangements is quite practicable. The thing to 
aim at ultimately is a return of the cases of sickness in the civil 
jwpulation as comi)lete as is now procured from the army in 
England. It Avill be an invaluable contribution to therapeutics, 
as well as to hygiene, for it will enable the therapeutists to deter- 
mine the duration and the fatality of all forms of disease under 



40 VITAL STATISTICS. 

the several existing systems of treatment in the various sanitary 
and social conditions of the peoj^le. Illusion will be dispelled, 
quackery, as completely as astrology, suppressed, a science of 
therapeutics created, suffering diminished, life shielded from many 
dangers. The national returns of cases and of causes of death 
will be an arsenal which the genius of English healers cannot fail 
to turn to account." 

Information Available. Apart from compulsory notification 
of infectious diseases, the following sources of information are 
available : — 

1. Under an order made by the Local Government Board in 
February, 1879, it is incumbent on all district and workhouse 
medical officers appointed since that date to furnish the medical 
officers of health with returns of pauper sickness and deaths, 
as well as to notify the outbreak of dangerous infectious disease. 
A similar obligation has been imposed upon medical officers of 
district schools appointed after June, 1879. By means of these 
returns of pauper sickness a fair estimate of the prevalence of 
disease among the poorest classes can be obtained. 

2. The keeper of a common lodging-house is bound to give 
information to the local authority of any case of dangerous 
infectious disease occurring on his premises. 

3. Where bye-laAVS are in force in any district in relation to 
houses occupied by more than one family, the householder may 
be compelled to notify the occurrence of infectious disease to the 
local authority. 

4. In addition to these sources of compulsory information, 
information is usually available from medical men where disin- 
fection or removal of patients is required, from the clergy, from 
school-lioard officers, and from the post-office authorities when any 
of their employees suffer from infectious illness. 

It is unfortunate that in the stress of modern political life the 
subject of a national system of notification and registration of 
sickness, except as regards the chief infectious diseases and certain 
industrial diseases, has been allowed to drop into abeyance. The 
compulsory notification of infectious diseases will be considered in 
the next chapter. 

What may be regarded as an ideal system is that in force in the 



REGISTRATIOX OF SICKNESS. 41 

army and navy, where every ca.se of sickness is tabulated as to 
character, duration, and result. Such a comi)lete system is im- 
practicable in civil life, and we will content ourselves Avith a series 
of proposals of what may Ije reasonably attempted so far as the 
general population is concerned. This nece.-sitates a short previous 
discussion of the scope of preventive medicine. 

To contend that preventive medicine is limited in its scope by 
the so-called zymotic diseases, is to rob it of its most important 
and promising field of work. Zymotic diseases * in the five years 
l.'^91-95 caused an average annual death-rate of 2757 per million 
living. In the same period rheumatic fever and rheumatism of 
the heart were responsible for an average death-rate of 88 per 
million ; endocarditis and pericarditis, which in a vast preponder- 
ance of cases are caused by rheumatism, causing a death-rate of 
.3.33 per million ; while tubercular disea.ses caused a death-rate of 
2123 per million (phthisis being respon.sible for 1464 of this); 
and bronchitis and pneumonia caused a death-rate of 3329 per 
million. Of the zymotic diseases a death-rate of 806 per million 
was caused by measles and whooping-cough collectively, of 415 
per milHon by influenza, and of 652 per million by diarrhrx-a and 
cholera. Xone of these is included in the scope of compulsory 
notification of infectious diseases as enforced in the majority of 
districts ; and although it may be doubted whether any immediate 
])ractical benefit would arise from such notification, the improved 
knowledge of their natural history and causation, which would 
gradually accumulate, must in the end prepare the way for more 
effective preventive measures. At present, with the possible 
exception of summer diarrhoea, it may be said of these diseases 
that the sanitar}' measures already adopted in this country have 
produced but little, if an}', eff'ect. If we omit these diseases, there 
remains a death-rate of 884 per million due to infectious diseases, 
the spread of some of which has been seriously combated by 
sanitary authorities. The total anniliilation of the latter diseases 
would only have reduced the general death-rate, in 1891-95, from 
18-74 to 17-86 per 1000; while the annihilation of tubercular 
diseases, which is much more within the range of possibility, and 
may in fact be accomplished, like the already secured annihilation 
as an endemic disease of the closely allied disea.se leprosy in this 

* Including small-pox, measles, scarlet fever, typhus, enteric and con- 
tinued fever, whooping-cough, influenza, cholera, diarrhffia, nialaria, hydro- 
pliobia and other zoogenous diseases, venereal diseases, erysipelas, puerperal 
fever, and other septic diseases. 



42 VITAL STATISTICS. 

country, would have reduced the general death-rate in 1891-95 
from 18-74 to 16-62 per 1000. The mortality really caused by 
rheumatic fever and its sequelse is immensely understated by the 
421 per million officially ascribed to rheumatic fever, endocarditis, 
and pericarditis. This disease will probably ere long come into 
the list of actively preventible diseases. A very large amount of 
bronchitis and pneumonia is caused by improper conditions of 
housing or of work ; and there is little doubt that a large saving 
might be effected under this head. Alcoholism figures low in the 
official returns, 68 deaths per million being ascribed to this cause 
in 1891-95; and even if we add the death-rate of 120 per million 
caused by cirrhosis of the liver (an almost entirely alcoholic 
disease), the official returns give a very incomplete notion of the 
immense mortality due to this preventible cause. These instances 
by no means exhaust the list which might be given to illustrate 
the fact that preventive medicine is concerned Avith all the diseases 
to which flesh is heir, the only condition beyond its possible scope 
being old age. 

Proposals as to National Notification and Registration of 
Sickness. Accurate knowledge of sickness, of its degree of inci- 
dence in relation to sex, age, occupation, housing, locality — in fact 
of all the conditions under which it is originated— must precede 
rational preventive measures. Hence • it is necessary that the 
following measures should be adopted : — 

1. All cases of sickness occurring among the 'parochial jjoor in 
each district should be periodically reported to the medical officer 
of health, and tabulated statements concerning them forAvarded 
to a central office in London, in which such statistics, along with 
those from other sources, should be analysed, summarized, and 
published. 

Schedules might easily be arranged similar to those in force in 
Christiania or Berlin, in which a Aveekly return of the new cases 
of sickness among the poor could be made by the Poor-LaAv 
medical officer with a minimum of trouble. The cases in the 
workhouse infirmaries and in industrial schools should be similarly 
scheduled. Care would be required to prevent the same cases 
from being entered more than once. The machinery necessary for 
the carrying out of this proposal already almost completely exists, 
(See p. 40.) 

2. All cases of sickness, wJiether out-patients or in-patients, at 



REGISTRATION^ OF SICKNESS. 43 

hospifah {general and special) and at pidjlic dispensaries should be 
reported weekly to the medical officer of health, and a summary 
forwarded by him to the central office in London, to be there 
treated like the pauper statistics. The hospitals and dispensaries 
of this country are supported by subscriptions or bequests ; and it 
would, I think, be reasonable to require that every public institu- 
tion for the treatment of the sick should give to the medical 
officer of health a weekly statement of the number of new in- 
patients and out-patients treated during the week, specifying the 
age, sex, and nature of the illness of patients ; also a quarterly or 
annual statement of the total cases, and the number of days spent 
by each patient in the hospital. The statistics of large general 
hospitals, especially those to which medical schools are attached, 
are of great value, the diagnosis and certification being excep- 
tionally accurate. These statistics possess a high value in the 
study of the annual and seasonal incidence of diseases like 
rheumatic fever, as I have shown in the Milroy Lectures for 
1895.* 

It is particularly unfortunate that in so many hospitals classified 
records of cases have not been regularly kept. 

It should be made obligatory on the managing bodies of all 
general and special hospitals, and all public dispensaries, to keep 
accurate entries of all cases treated at these institutions, as well as 
to report on special schedules these cases to the medical officer of 
health at stated intervals. This has been done in Germany since 
1877.t 

Many important problems as to the intensity of difl'erent epide- 
mics, the relative fatality of cases occurring in different districts, 
the influence of "hospitalism" on the character of each disease, 
etc., might be solved by accurate comparative statistics for the 
great fever hospitals throughout the countr3^ At present there 
are statistical reports for such hospitals in the annual reports of 
some medical officers of health, of very varying comprehensiveness 
and value. What is required is that these should be collated on a 
uniform basis, and that the statistics from different hospitals should 
be analysed and published at a central office in London. 

The annual reports of the Statistical Committee of the Metro- 
politan Asylums Board, the report for the year 1896 being the 
eleventh of the series, form in some respects a model for others. 

* The Lancet, March, 1895. 

t For particulars see my paj^er in the lioycd Statist. Soc. Jour., vol. lix. 
part. i. p. 16. 



44 VITAL STATISTICS. 

3. All Friendly Societies, and all sickness insurance societies of 
every description should be required to furnish weekly or monthly 
returns of the number of new cases of sickness in their experience, 
classified according to a specified schedule, and a yearly statement 
of the total number of subscribing members, classified according 
to age. 

Such Friendly Societies are already under some degree of 
control as regards their financial condition, and accurate statistics 
of sickness might be required in the interest of the community. 
These would furnish a very valuable means of estimating the 
relative amount of yearly sickness at difi'erent ages in the in- 
dustrial classes, the relative incidence of special diseases at certain 
ages and in special occupations, and so on. Such statistics would 
throw a flood of light on the healthiness or the reverse of various 
industries, and would open the way for valuable preventive 
measures.* 

4. An attempt slioidd he made to obtain accurate returns of sick- 
ness in the great industries. This can only be gradually secured. 
Two factors are necessary in order that industrial sickness may be 
estimated for comparative purposes : (a) an accurate return of the 
number of men employed in each industry ; and (h) a similarly 
accurate return of the cases and causes of sickness ; each classified 
according to age. Some important steps have been taken in this 
direction in the Factory and Workshops Act, 1895. By sec. 34 it 
is required that — 

The occupier of every factory and workshop shall, on or before 
the 1st day of March in every year, send to the insjjector of the 
district on behalf of the Secretary of State a correct return specifying, 
with resjiect to the year ending on the preceding 31st day of December, 
the number of persons employed in the factory or workshojD, with 
such ^particulars as to the age and sex of the persons employed as 
the Secretary of State may direct, and in default of complying with 
this section shall be liable to a fine not exceeding £10. 

There is no provision requiring a general notification of sickness 
among the employees, although this would be quite practicable. 

* It is true that at present there is great discrepancy in the administration 
of Friendly Societies and in the amount of sickness which their experience 
shows in persons of corresponding ages. The data from these societies would 
consequently require to be judiciously employed for many years to come. 
The proposed collation and tabulation and publication of the experience 
of these societies would, however, probably form the first step in the direction 
of securing more uniform administration of sick relief in different localities. 



REGISTRATION OF SICKNESS. 45 

The only approach to it are the enactments contained in sec. 20 
and sec. 29. 

Sec. 20 states that — 

(1.) Every occupier of a factory or workshoji shall keep a register of 
accidents, and shall enter therein every accident occurring in the 
factory or workshop, of which notice is re(piired hy the Factory Acts 
within one week after the occurrence of the accident, and this register 
shall he at all times open to inspection by the inspector and the 
certifying surgeon for the district. 

(2.) If any occupier of a factory or workshop makes default in 
complying with the requirements of this section, he shall he liable on 
summary conviction to a penalty not e.xceeding £10. 

This enactment will doubtless be of great value in determining 
the relative liability to accidents of different industries, and the 
directions in which additional regulations and restrictions are 
required. 

Sec. 29 requires that — 

(1.) Every medical practitioner attending on or called in to visit a 
patient whom he believes to be suffering from lead, phosphorus, or 
arsenical poisoning, or anthrax, contracted in any factory or workshop, 
shall (unless the notice required by this section has previously been 
sent) send to the Chief Inspector of Factories at the Home Office, 
London, a notice stating the name and full postal address of the 
patient, and the disease from which, in the opinion of the medical 
practitioner, the jiatient is suffering, and shall be entitled in resj)ect of 
every notice sent in pursuance of this section to a fee of 2s. 6d., to Ije 
paid as part of the expenses incurred by the Secretary of State in 
the execution of the principal Act. 

(2.) If any medical practitioner, when required by this section to 
send a notice, fails forthwith to send the same, he shall be liable to 
a fine not exceeding 40s. 

(3.) Written notice of every case of lead, phosphorus, or arsenical 
poisoning, or anthrax, occurring in a factory or workshop, shall forth- 
with be sent to the inspector and to the certifying surgeon for the 
district ; and the provisions of the Factory Acts with respect to acci- 
dents shall apply to any such case in like manner as to any such accident 
as is in those sections mentioned. 

(4.) The Secretary of State may by order made in accordance with 
sec. 65 of the princii^al Act apply the provisions of this section to 
any other disease occurring in a factory or a workshop, and there- 
upon this section and the provisions referred to therein shall apjjly 
accordingly. 

The provisions in sec. 29 constituted at the time they were 
enacted a new and evil departure, that of compulsory notification 



46 VITAL STATISTICS. 

of disease by a medical practitioner to a layman,* implying, in 
part at least, the investigation of the medical problems of the 
causation of special diseases by lay inspectors. The objection has 
since been diminished by the appointment of Dr. Whitelegge 
as H.M. Chief Inspector of Factories, and later by the appoint- 
ment of Dr. Legge as Medical Inspector of Factories. There can 
be little doubt that as more attention is paid to the important 
subject of industrial hygiene it Avill be necessary to arrange for 
the local medical officer of health to receive in the first instance 
the notifications under sec. 29, and conduct the primary inquiries 
arising out of these. The transfer of control of Bakehouses from 
the central to local authorities is a somewhat analogous case. 
To sum up : — 

(a.) All cases of sickiiess treated at the expense of public 
funds, whether in connection with the administration of the Poor 
Law (out-door infirmaries, industrial schools, etc.) or in isolation 
hospitals, or in idiot and lunatic asylums, should be periodically 
notified to the medical officer of health. 

(b.) All cases of sickness treated by means of public charity, 
whether in general or special hospitals or dispensaries, should be 
similarly notified. 

(c.) All cases of sickness treated in Friendly Societies or other 
sickness assurance societies should be similarly notified. 

(d.) Keturns of accidents and of certain diseases, as lead 
poisoning, woolsorters' disease, etc., or other industrial diseases, 
should be made part of a wider system of notification of diseases 
by private medical practitioners to the medical officer of health of 
each district. 

(e.) All notifications of sickness should be sent in the first 
instance to the medical officer of health of each district, and by 
him transmitted to a central office in London. 

(/.) The central office in London should probably be in con- 
nection with the General Eegister Office, Somerset House, and 
weekly returns of sickness should be published alongside of the 
weekly returns of mortality. 

* For further particulars on this point see communications from Dr. J. B. 
Russell of Glasgow, and from the author in the British Medical Journal, 
31st August and 10th September, 1895. 



CHAriEK VI. 

THE COMPULSORY NOTIFICATION OF INFECTIOUS 
DISEASES. 

rpiIE primary object of registration of sickness is prophylactic, 
J. and from this standpoint the registration of infectious diseases 
is su})remely important. Such registration, in order to be of vahie, 
must be compulsory. Whenever it has been simply voknitary 
and optional the returns have been invariably imperfect and in- 
complete. Voluntary notification has been tried in a few places, 
medical men being paid a fee for every case information of Avhich 
the}^ furnish to the sanitary authority. The result has been only 
very partial. The medical practitioner is by possibility subjected 
to odium and accused of a breach of professional secrecy when 
he notifies, unless the notification is compulsory. Such partial 
information is not trustworthy as indicating the prevalence of 
a disease, though it is better than none ; nor is it so efiicacious in 
stopping the spread of disease. The more cases the medical 
officer of health knows of, and the wider the basis on which 
his etiological inductions can be framed, the more likely are 
preventive measures to be successful. It must not be sup2>osed, 
however, that compulsory notification of infectious diseases forms 
a complete means of meeting and combating infectious diseases. 
" We do not only seek to suppress them when they arise, but to 
prevent their origin " (Ransome), and to this end we require 
to study thoroughly their natural history, their habitats, and the 
conditions under Avliich they develop and recur. 

The notification of infectious diseases became actual fact in a 
characteristically British fashion. The experiment was allowed 
to be made hj those towns desiring to make it. In September, 
1877, the first local Act for enforcing the compulsory notification 
of the chief infectious diseases came into operation in Bolton, 
Lancashire. This example was followed by other towns, and the 
adoptive enactment of the Infectious Diseases (Notification) Act 

47 



48 VITAL STxVTISTICS. 

in 1889 was followed by a rapid adoption of the Act by urban 
and rural sanitary authorities throughout England. At the present 
time the Act applies to more than five-sixths of the English 
population, and there is little doubt that it Avill shortly be made 
compulsory throughout the whole of Great Britain. 

In some of the earlier local Acts notification was (a) compulsory 
only on the householder (Greenock) ; (h) compulsory only on 
the medical attendant {e.g., Manchester, Preston, Edinburgh, 
Aberdeen) ; Avhile in three towns (Bradford, IsTorwich, and 
Nottingham) (c) it was made compulsory on the medical 
attendant to furnish a certificate of the disease to the householder, 
the latter being responsible for its transmission to the local 
authority. In most of the towns possessing local Acts the parent 
or occupier of the house is bound to give notice to the local 
authority in case no medical man is in attendance. 

Provisions of the Infectious Disease (Notification) Act, 1889. 

Adoption of the Act. This is a permissive or adoptive Act, which 
may be adopted by any sanitary authority by a resolution passed at a 
meeting of the authority after fourteen clear days' notice (sec. 5). In 
London alone it became immediately compulsory Avithout any option, 
being replaced in the metropolis at the beginning of 1892 by similar 
enactments in the Public Health (London) Act, 1891. 

Definition of Infectiotis Disease. The expression "infectious disease" 
applies to the diseases enumerated in the certificate on page 50, and 
any other infectiou? diseases to Avhicli this Act has been applied as 
provided under sec. 7 (sec. 6).* 

Extension of Act to other Infectious Diseases. Any local authority may, 
after fourteen days' notice given as the result of a special resolution 
passed by the authority at a previous meeting— as in the original 
adoption of the Act — order that the Act shall apj^ly to any other 

* No definition is given of puerperal fever, and as according to the last 
edition of the Nomenclature of Diseases (1896, p. 11) the term "puerperal 
fever" should no longer be used, some latitude must be exercised as to what 
comes properly under this name. The Nomcnelature adds " pyaemia, septi- 
caemia, or sapracmia, occui'ring in puerperal women should be described as 
'puerperal pyaemia,' ' septicaemia,' or 'sapraemia,' respectively." A Com- 
mittee of the Royal College of Physicians of London has reported (Dec., 
1898) that with a view to the limitation of dangerous infectious diseases the 
London Comity Council would be acting rightly in adopting the view that 
the expression " puerperal fever " should be taken to include septicaemia, 
pyaemia, septic peritonitis, septic metritis, and other acute septic inflam- 
mations in the pelvis occurring as the direct result of child-birth. 



NOTIFICATION OF INFECTIOUS DISEASES. 49 

infections disease than those enumerated under sec. 6 [sec. 7 (1)]. Any- 
such order may be permanent or temporary, the period to be specified 
in the hxtter case. The order under this section and the revocation or 
any variation of this order shall not be valid until approved by the 
Local Government Board [sec. 7 (2) and (3)]. In the case of emer<fency 
three clear days' notice under sec. 7 shall be sufficient, but the resolution 
of the local authority shall declare the cause of such emergency and 
shall be for a temporary order [sec. 7 (6)]. 

Notice of Adoption. Public notice must be given of the adoption of 
the Act and of all modifications of it, and eveiy registered practitioner 
residing or practising within the district must receive a copy of such 
notice [sec. 5 (2) and sec. 7 (5)]. 

Method of Notification. Where an inmate of any building used for 
human habitation within a district to which this Act extends is 
suffering from an infectious disease to which this Act applies, then, 
unless such building is a hospital in which persons suffering from an 
infectious disease are received, the following provisions shall have 
effect : — 

(«) The head of the family to which the patient belongs, and in his 
default the nearest relatives of the patient in the building or in 
attendance on the patient, and in default of such relatives every 
person in charge of, or in attendance on, the patient, and in default of 
any such person the occupier of the building, shall, as soon as he 
becomes aware that the patient is suffering from an infectious disease 
to which this Act applies, send notice thereof to the medical officer of 
health of the district. 

(6) Every medical practitioner attending on, or called in to visit the 
patient, shall forthwith, on becoming aware that the patient is suffering 
from an infectious disease to which this Act applies, send to the 
medical officer of health for the district a certificate stating the name 
of the patient, the situation of the building, and the infectious disease 
from which, in the opinion of such medical practitioner, the patient is 
suffering. 

Every person not complying with the above requirements is liable, 
on conviction, to a fine not exceeding 40s. ; provided that if a person is 
required as above to notify only in default of some other person, he 
shall not be liable to any fine if he satisfies the Court that he had 
reasonable cause to suppose that the notice had been duly given. 

Remuneration for Notification. The Local Government Board may 
from time to time prescribe forms for the purpose of certificates under 
this Act, and these forms must be used in certifying cases [sec. 4 (1)]. 

The folloAving is the form at present prescribed : — 



60 



VITAL STATISTICS. 



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NOTIFICATION OF INFECTIOUS DISEASES. 51 

The local autlioiity is required to supply these forms to medical 
practitioners, and to pay to every medical practitioner for each certifi- 
cate duly sent by him in accordance with this Act a fee of 2.s. Gd. 
if the case occurs in his private practice, and of Is. if the case occurs 
in his practice as medical officer of any public body or institution 
[sec. 4 (2)]. 

These certificates may be sent by being left at the office or residence 
of the medical officer of health, or may be sent by post addressed 
to him [sec. 8 (2)]. 

Exem})tio7is under the Act. The i)rovisions of this Act apply to 
every ship, Ijoat, tent, shed, etc., used for human habitation [sec. 13 (1)], 
except shi2)s and boats belonging to any foreign government. All 
buildings, vessels, tents, etc., belonging to H.M. the Queen are exempt 
from the terms of this Act (sec. 15). 

Notification under the Public Health (London) Act, 1891. 

The cliief regulations are identical with those of the Infectious 
Disease (Notification) Act, with the following exceptions : — 

The medical i)ractitioner is required to certify the age and sex 
of the i)atient and whether the case has occurred in private or jjublic 
practice, as well as the usual particulars [sec. 55 (1) (h)]. 

The medical officer of health must, within twelve hours of the 
receipt of a notification certificate relating to a metropolitan patient, 
send a copy thereof to 

(a) The Metropolitan Asylum Managers ; 

(b) The head teacher of the school attended by the patient if a 
child, or by any child who is an inmate of the same house as the 
patient [sec. 55 (4)]. 

Advantages of Compulsory Notification. The prompt and 
complete information furnished by this means 

(a) Enables the medical officer of healtli to take immediate 
measures to prevent the spread of infection ; by enforcing proper 
isolation of patients at home or in an isolation hospital ; by 
enforcing elficient disinfection of infected articles and persons, 
including proper methods of disposal of the infected dead ; by 
vaccinating those who have been exposed to the infection of 
small-pox ; and by preventing the attendance of children in 
school or of adults in workshops from infected houses. 

(h) It further enables the cause of an outbreak of an infectious 
disease to be investigated with a good chance of success. In 
its absence many of the links of evidence are missing. Thus the 
influence of water-supply, milk, or any other infected food-supply, 



52 VITAL STATISTICS. 

of personal infection in school, workshop, laundry, etc., can be 
ascertained, and the influence of sanitary conditions of special 
localities or houses can be investigated. 

(c) Not the least value of notification consists in the educa- 
tional efi'ect of the necessary inspections upon parents, house- 
holders, teachers, etc., and its still greater educational effect upon 
the members of local authorities. The constant reiteration of the 
lesson taught by the notification certificates has gradually and 
increasingly stimulated local authorities in the discharge of their 
duties. Hence it is not surprising to find that at no previous 
period of the sanitary history of England has there been such 
great activity as since 1889 in the provision of isolation hospitals. 
If these isolation hospitals had not, by the removal of first cases 
of infectious diseases in houses, diminished the prevalence of 
infectious diseases, they have as humanitarian institutions justified 
their existence by the better and more successful treatment that 
the majority of patients thus removed have secured; but they 
have also diminished the actual amount of some of these diseases. 
Small-pox epidemics are more easily manageable, and have been 
kept within narrower bounds in communities in which all cases 
are notified and isolation enforced. A portion of the greatly 
diminished fatality of scarlet fever is ascribable to the fact that 
patients are treated in a much higher proportion in large, airy, 
hospital wards, instead of in crowded houses with imperfect 
nursing. 

(d) Even if it could be shown that compulsory notification of 
infectious diseases had not prevented radiation of disease from 
a single focus of infection, and had not led to the discovery of 
a single evil condition competent to produce further disease, the 
continued operation of the Act would be desirable from a wider 
standpoint. AVe are, by means of notification, gradually accumu- 
lating throughout the country a mass of information as to the 
seasonal, annual, epidemic, and cyclical prevalence of the chief 
infectious diseases such as has never previously been possessed 
by epidemiologists. As the first condition of success in the 
prevention of disease is knowledge ' of its natural history — its 
epidemicity, its relation to age and sex, to social and industrial 
conditions, to the complex meteorological conditions embodied in 
the words "season and climate" — such an accumulation of infor- 
mation must ere long bear fruit of a practical, useful character. 
Medical officers of health are not mere empiricists, concerned 



NOTIFICATION OF INFECTIOUS DISEASES. 53 

with the enforcement of general cleanliness, and of disinfection 
and isolatiDU wlien cases of infectious disease arise. They are 
concerned not solely with individual cases of disease, but also 
with the conditions producing and controlling entire epidemics. 
It is in this branch of their work that knowledge is as yet most 
imperfect ; and it is only by the accumulation of accurate and 
complete information as to each epidemic and inter-epidemic 
l)eriod, and by the collateral study of the personal and environ- 
mental conditions associated with these periods, that we can hope 
to arrive at a less empirical and more rational conception of the 
causation of each infectious disease, and through that of its 
prevention. 

Effect of Notification on Zymotic Mortality. Attempts have 
been made to determine by appeal to figures whether compulsory 
notification diminishes the prevalence and fatality of infectious 
diseases. We doubt whether such an appeal to figures can be 
trusted, because it is hardly possible that the periods compared 
should fulfil an indispensable condition Avhen comparisons are 
instituted ; viz., that other tilings sliall he equal. Notification 
is but a means to an end. In some towns the information fur- 
nished by it has been made the basis of active and persistent 
preventive work, while in others this has not been so. The 
question is mixed up also with that of hospital accommodation 
and isolation. There may be no immediate good results from 
notification if the patients notified cannot be properly isolated. 

Furthermore, after such a disease as measles or scarlet fever 
has gone through a town it exhausts the supply of persons "prone 
to these diseases; and apart altogether from any sanitary measures, 
some years may elapse before sufficient material has accumulated 
to furnish fuel for another outbreak. In addition to this, there 
are cyclical influences, the nature of which is imperfectly known, 
but which have important bearings on the prevalence of a given 
disease. So that neither, on the one hand, the comparative 
absence of a given infectious disease since notification came into 
force, nor, on the other hand, its increased prevalence, necessarily 
proves the utility or inutility of notification. 

It should be remembered also that the materials available for 
drawing conclusions are very scanty, and that in many towns 
the period since notification began is too short to enable valid 
conclusions to be drawn. 

In attempting comparisons of death-rates from a particular 



54 VITAL STATISTICS. 

infectious disease between periods before and after compulsory 
notification was enforced, the following precautions must be 
particularly regarded : — 

(1) Avoid average statements for groups of years. In treating 
of epidemic diseases no method is so likely to conceal the truth 
as this. In connection with small-pox statistics it has led to 
numerous errors. In other infectious diseases it is frequently 
quite practicable to show an increase or a decrease of mortality 
by adjusting the groups of years. The only proper method is to 
compare year by year, if practicable in a long series, and the data 
necessary for this can be best displayed by making a cvirve of the 
annual death-rate for the jDeriod under comparison, 

(2) Remember that, as in scarlet fever, the mortality from a 
disease may decline to a much greater extent than its prevalence. 

(3) Note that in view of the fact that the birth-rate in England 
is declining, and the age distribution of the population is con- 
sequently becoming modified, it is desirable in exact inquiries 
to state the amount of infectious disease at different age-groups 
for successive years in proportion to the number living at each 
age-group. This is especially important for the diseases occurring 
chiefly in infancy, as diarrhoea, the amount of which may be 
grievously misrepresented if it is stated in proportion to the popu- 
lation living at all ages, and not in proportion to the infantile 
population. 

National Registration of Infectious Diseases. The possession 
by each medical officer of health of information as to the amount 
and nature of the infectious diseases prevalent in his own district 
does not exhaust the possibilities of utility of these returns. 
Their value would be greatly increased by collateral information 
as to the amount and nature of the infectious diseases prevalent 
in neighbouring districts and in the rest of the country, or even 
in other countries. By such an interchange of prompt and 
trustworthy information it would be practicable to forecast the 
possibilities of the introduction into a community of a given 
disease, and take suitable precautions. This defect in local 
notification was soon seen, and at the beginning of 1888 Dr, ^ 
Tatham, then medical officer of health of Salford, made a private 
arrangement with the medical officers of health of thirty-two 
other notification-towns, by which he should receive from them 



NOTIFICATION OF INFECTIOUS DISEASES. 55 

weekly returns of tlie cases notified in each town. These were 
tabulated by him, and circulated confidentially amongst the con- 
tributing medical officers early in the succeeding week. The 
practicability and the utility of this voluntary inter-notification 
having been fully established, many of the local authorities of 
the towns concerned petitioned the Local Government Board to 
take the matter in hand as a "going concern"; and in 1889 
the IJoard undertook the tabulation and distribution of the 
statistics of cases of sickness notified to the medical officers 
of health of those towns in which the notification of infectious 
diseases is compulsory. Only the co-operating towns receive the 
table summarizing the statistics of these notification- towns ; and 
it is marked "not for publication."* We may reasonably hope, 
however, that this beginning will ere long end in a national 
registration of infectious diseases, and a similar tabulation and 
distribution of the national statistics. On two occasions depart- 
ments of the Government have tabulated and circulated returns 
of sickness : first, metropolitan sickness of all kinds in 1857, and, 
secondly, infectious diseases in contributing notification-towns from 
1889 onwards. These facts establish a valuable precedent, and 
furnish hope that a governmental department may soon be induced 
to take up in a much more complete and general form the collation 
of the general sickness statistics of the community, so far as they 
can be made available. 

Suggestions as to Notification of Infectious Diseases. The 

notification enforced in the Infectious Disease (Notification) Act 
is "dual." The advantage of this is that the householder being 
associated in compulsion with the medical practitioner, the latter 
avoids any possible odium. The chief disadvantages are that 
(a) the dual method will, in the event of secrecy being desired, 
prevent a medical man being called in. This has not been found 
to operate largely in actual fact ; and even if so, the same thing 
would happen if the onus of notification rested solely on the 
householder, (h) The fact that the householder is bound to 

* The annual report of tlie medical officer to tlie Local Government Board 
embodies a talailar statement of tlie number of notified cases and registered 
deaths from the notifiable infectious diseases in each of eighty-one urban 
sanitary districts quarter by quarter, and a weekly statement of the same 
facts for each of the sanitary districts of London (]ip. 119-172, Report for 
1895-96). The utility of this return would be greatly increased if it were 
published as a separate document at an earlier period than the entire report 
of the medical officer can be issued. 



§6 VITAL STATISTICS. 

notify " as soon as he becomes aware " that a patient is suffering 
from a notifiable disease presupposes some medical knowledge on 
his part, an assumption the advisability of which most medical 
men Avould doubt. Where a medical man has notified, notification 
by the householder has always been practically a dead letter ; but 
what of cases for which no doctor is called in? It is usually 
impracticable to obtain in such cases a conviction for non-notifica- 
tion, because there is no provision in the law throwing the onus 
of proof of ignorance on the householder. 

It is very desirable that the present machinery of the Infectious 
Disease (Notification) Act should be made more elastic and more 
comprehensive. In Germany and Scandinavian countries diseases 
are classified into two categories,* according as immediate or 
weekly notification is required. Such a grouping would enable a 
considerable extension of notifiable diseases in this country with- 
out commensurate increase of expense. Among the less urgent 
diseases for which a monthly or weekly notification would suffice 
would come tubercular diseases, especially phthisis. The time is 
ripe for greatly extended preventive measures against the spread 
of tuberculosis. 

* For particulars see paper by the author, Jour. Eoijal Statist. Soc. , vol. 
lix. part i. 



CHAPTEK VII. 



MARRIAGES. 



MARRIAGE statistics possess great interest for all who are 
concerned Avith the Avelfare of the people, affording as they 
do a valual)le index of national prosperity, and incidentally in 
England tlirowing an interesting light on the progress of elemen- 
tary education. 

Estimation of Marriages. (1) The usual method is to state 
the proportion to the actual ])opulation, or the number per 1000 
living. Although this method is fairly reliable in comparing the 
same town or community in successive years, it might lead to 
some inaccuracy if employed in comparing different communities 
in the same year, inasmuch as, owing to varying age and sex 
constitution and other circumstances, the number of marriageable 
persons living in different communities' must vary considerably. 

In the following table the highest and lowest marriage-rates in 
the chief European countries are given. The variations of the 
marriage-rate in each country may be studied in further detail 
by consulting Tables 44-61, pp. .115-122, in the Registrar- 
GeneraVs Annual Report, 1896. 

Markiage-Rate (Persons Married) per 1000 of Population 
SINCE 1864. 





Highest. 




Lowest. 


Hungary 


20-8 in 1S79 


16'3 in 1889 (since 1876) 


Austria 


. 20-7 „ 1869 


15-1 


, 1877 and 1890 


Prussia 


. 20-7 „ 1872 


14-8 , 


, 1870 (year of war) 


France 


19-5 ,, 1872 


12-1 , 


, 1870 (year of war) 


Switzerland 


18-0 ,, 1875 


13-7 , 


, 1880-82 (sincel871) 


Denmark . 


17-8 ,, 1865 


13-6 , 


, 1891 


England and Wales 


17-6 „ 1873 


14-2 , 


, 1886 


The Netherlands 


17-1 „ 1873 


13-8 „ 1888 


Italy 


16-8 ,, 1875 


11-3 , 


, 1866 (since 1866) 


Norway 


15-7 „ 1875 


12-2 , 


, 1888 (since 1871) 


Belgium 


15-7 „ 1866 


13-4 „ 1878 and 1886 


Scotland 


15-5 „ 1873 


12-6 , 


, 1886 


Sweden 


14-6 ,, 1873 


10-9 , 


, 1868 


Ireland 


10-9 ,, 1865 


7-8 , 


, 1880 



57 



58 VITAL STATISTICS. 

(2) The more accurate method of calculating the marriage-rate 
for comparative purposes is to base it on the number of bachelors, 
spinsters, widowers, widows, and divorced persons living at 
marriageable ages. The number of these can be obtained for 
the census year from the census returns for each registration and 
sanitary district in England (^Census RepoJ't, 1891, vol. iii.), and it 
may be assumed that the same method of estimation for increase 
of this portion of the population can be adopted as that described 
(p. 6) for the whole population. 

The question arises whether the relative place of the above 
countries would be altered were this more accurate method of 
calculating the marriage-rate adopted. Dr. J. Bertillon* has 
calculated for many European countries the number of persons 
married annually per 1000 marriageable persons, i.e., persons 
over fifteen years of age who are celibates, divorced persons, or 
widowed. The highest on the list is Hungary (72 '6), next come 
in order Saxony (60"8), Prussia (51*0), England and Wales (50-2), 
Denmark (47-9), Italy (47-5), France (45-4), Belgium (40-0), 
Scotland (39-6), Sweden (36-9), and Ireland (23-1 per 1000 
marriageable persons over fifteen years of age). 

The above rates are calculated on the returns for each country 
for the years 1878-82. The high marriage-rate in Hungary is 
ascribed by Dr. Bertillon to the frequency of remarriage of 
widowers, and indirectly to the high mortality in that country. 
Judging by the marriage-rate per 1000 of total population, 
Hungary is surpassed by the purely Slavonic races of Croatia- 
Slavonia, Servia, and Russia. 

Calculated by either of the above methods, Hungary shows 
the highest marriage-rate among the countries for whom exact 
figures are given above and on page 57 ; Prussia is high in both, 
while the marriage-rate of England and Wales is, from a com- 
parative standpoint, much higher, and that of Prance lower, when 
calculated by the more accurate method. 

Condition as to Marriage of the English Population. 

Between 1881 and 1891 the average annual marriage-rate was 
very considerably lower than that of the immediately preceding 
decennium. jS'otwithstanding this the proportion of married and 
widowed persons in the population did not show any marked 
decline, as may be seen from the following table : — 

* J^^Umcnls dc Democfraphie, 1896, p. 33. 



MARRIAGES. 



59 



Proportion of Single, Married, and Widowed Persons in 
THE Population per 1000 living, 1881 and 1891. 



Year. 


Males. 


Females. 


Bachelors. 


Husbands. 


Widowers. 


Spinsters. 


Wives. 


Widows. 


18S1 
1891 


620 
620 


346 

345 


34 
35 


592 
596 


333 
329 


75 
75 



This seeming paradox is explained l)y the fact that, althougli 
a decline of the marriage-rate diminishes the proportion of married 
men and women in the po^ndation, it also diminishes the propor- 
tion of the unmarried by causing a lowered birth-rate. The 
varying degree of migration among married and unmarried, and 
the varying degree of lowering of the deatli-rate at ditl'erent age- 
groups, have co-operated in producing the above result. 

Of the male population of all ages at the 1891 census 35 per 
cent, were married men, while of the female population only 
33 per cent, were wives ; if widowed persons are also taken into 
account, the proportions become 38 jier cent, for the men and 
40 per cent, for the women. 

Higher Marriage-Rate in Towns. The man-iage-rate is always 
higher in large towns than in rural districts. This is chiefly 
explained by the fact that a large number of young country- 
people resort to populous districts, where, owing to the presence 
of large trades and manufactures, higher wages can be secured, 
and there they marry. In towns there is nearly always an excess 
of persons l^etween twenty and forty years of age. Many also 
resort to toAvns merely to be married, subsequently returning to 
rural districts. 

Influence of National Prosperity on Marriage-Rate. Dr. 

Farr has described the marriage-rate as the barometer of 
prosperity (present in part, but future anticipated prosperity 
in still greater part), just as the funds are the barometer of 
credit. So we find that the marriages of England increase as 
"the result of peace after war, abundance after dearth, high 
wages after want of employment, speculation after languiil 
enterprise, confidence after distrust, national triumphs after 
national disasters." 



60 VITAL STATISTICS. 

The same conclusion is borne out by the fact, frequently 
alluded to by the Registrar-General in his reports, that the 
marriage-rate varies in the same direction as the value of British 
exports, the average price of wheat, and the amount per head 
of population cleared out at the Bankers' Clearing House. The 
coincidence, it should be pointed out, is one in direction, but not 
in degree. (See Table A. p. vi. Registrar-GeneraV s Anmial Report, 
1896.) The subject is ably discussed in a paper by Dr. W. Ogle 
{Jour. Royal Statist. Soc, vol. liii. part ii. 1890). 

Decline of Marriage-Rate. Notwithstanding the increasing 
wealth of the country the marriage-rate has declined, with inter- 
mittent smaller rises, from a maximum of 17-6 in 1873 to 15-0 
in 1895. It is probable that the steadily increasing standard of 
comfort among all classes, rendering men and women unwilling to 
undertake the responsibilities of family life without an assured 
income, has been chiefly instrumental in bringing this about. A 
similar decline has occurred in other countries. In France, 
Prussia, and the German Empire it set in a year earlier than 
in England. In the former countries the diminution appears 
greater, owing to the abnormally high marriage-rate in 1872, at 
the conclusion of the Eranco-Prussian war. 

Marriage Calendar. The Registrar-General's statistics show 
that most marriages occur in December, October, April, and June. 
The greater number of marriages in December, April, and June 
are accounted for by the festive periods of Christmas, Easter, and 
Whitsuntide coinciding with these months ; while October is the 
period after the harvest, when the agricultural labourer has 
comparative leisure as well as money in his pocket. The month 
of May, owing to a widespread superstition that it is an unlucky 
month for marriages, is lowest on the list.* The favourite days 
in the week for marriages are Saturday, Monday, and Sunday. 

Marriages and Remarriages. In 1896, of the total marriages 
of men 89-7 per cent, were of bachelors and 10-3 per cent. 

* Mr. S. A. Matthew, of Cambridge, writing to the author on this point 
in 1895, states : " I think that this is doubtless a survival of an old Pagan 
superstition. Brand tmce refers to it in his Popular Antiquities, ed. 1849, 
i. 224, ii. 168. Ovid, in the Fasti, says : ' MenscB malum Maio nubere 
vulgus ait.' And in this month were held the Festival of Bona Dea and 
the Feasts of the Dead." 



MARRIAGES. 61 

of widowers. Of the total marriages of women 92-7 per cent, 
were of spinsters and 7-3 per cent, of widows. The proportion 
of Avidowed persons who remarry has steadily declined. Thus 



In 1000 Marria;j;es 


Widowers. 


Widows. 


138 


100 


113 


79 


103 


73 



1871-75 . 

1891-95 . 

1896 . 

Ages at Marriage. The English statistics under this head are 
imperfect, owing to the j^hi'i-i-ses "full age," "minor," "under 
age " heing frequently inserted in the register. There is,' how- 
ever, a steady improvement in this respect; for while in 1851 in 
63 per cent, of the total marriages the precise age of one or 
other of the contracting parties was not stated, in 1861 the 
proportion had fallen to 37, in 1871 to 29, in 1885 to 8-5, and in 
1895 to 2-4 per cent. 

Of the total marriages in 1895 in which the age of the con- 
tracting parties was stated, the mean age of the women married 
was 26-2 years, and of the men 284 years. Taking marriages 
and remarriages sei:)arately, the mean age of widowers married was 
44-3 years ; of Avidows, 40-5 years ; of bachelors, 26-6 years ; and 
of spinsters, 25-0 years. Postponement of marriage of course 
limits the childbearing period ; and a portion of the lowering of 
birth-rate Avhicli has occurred of late years may be ascribed to this 
cause. 

The mean age at marriage has been gradually rising since 1873. 
In that year there was great prosperity, and the marriage-rate 
was at its maximum, the mean age of bachelors at marriage being 
25-6 and of spinsters 24-2 years, the lowest recorded. Since 
then the mean age at marriage has gradually risen, the figures for 
1895 (see Table B. p. viii. Begistrar-GeneraVs Annual Report, 
1895) being the highest yet recorded. When the marriages are 
few in number they are also delayed to a somewhat later period 
of life. 

Mr. C. Ansell in his Statistics of Families in the Upj)er and 
Professional Classes (page 44) found that the mean age at marriage 
of bachelors of these classes during the period 1840 to 1871 Avas 
29-95 years. 

Further statistics as to average ages at marriage of bachelors 
and spinsters in occupational groups Avill be found on page viii. 
Registrar-GeneraVs Fortij-nintli Report, 1886. Comparing the tAvo 



62 



VITAL STATISTICS. 



extreme instances given in this report Ave have the following 
result : — 

Average Age at Marriage of 



Miners . . . . . 
Professional and Independent Class 



Bachelors. 
, 24-06 
, 31-22 



Spinsters. 
22-46 
26-40 



Thus Avith higher social status not only the average age at 
marriage, but also the difference betAveen the ages of husband and 
Avife increases. 

At the census of 1891 the number out of 1000 males and 
females respectively at each age-group Avho were married Avas as 
folloAvs : — 

Condition as to Mareiage of 1000 MxVles and op 1000 Females 
AT SUCCESSIVE Age-Periods, 1891 {Census Report, vol. iv. p. 34). 





Males. 


Females. 


Ages. 
















Single. 


Married. 


Widowed. 


Single. 


Married. 


Widowed. 


All ages 


620 


345 


35 


596 


829 


75 


Under 15 


1000 


— 


— 


1000 


— 





15— 


996 


4 


— 


980 


20 





20— 


806 


192 


2 


701 


296 


3 


25— 


343 


645 


12 


326 


653 


21 


35— 


147 


819 


34 


164 


761 


75 


45— 


100 


8-27 


73 


124 


706 


170 


55— 


84 


771 


145 


110 


573 


317 


65 & upwards 


73 


590 


337 


107 


319 


574 



Marriage of Minors. The proportion of marriages under age 
has shoAvn a steady decline, as Avill be seen from the folloAviug 
figures (Registrar-GeneraVs Fifty-ninth Rejjort, 1896) : — 

Marriages under age in 1000 Marriages. 





Men, 


Women. 


1871-75 . 


82 


223 


1876-80 . 


78 


217 


1881-85 . 


73 


215 


1886-90 . 


63 


200 


1891-95 . 


56 


183 


1896 . 


53 


174 



MARHIAGES. 63 

Signatures in Marriage Register. These throw an interesting 
side-hght on the state of elementary education in England, as 
indicated by the inahility to sign the marriage-register. 

In 1841, out of every 100 men married 33, and out of every 
100 women married 49, Avere nnal)le to sign the marriage-register. 
The proportion has steadily declined, until, in 1895, only 4'0 per 
cent, of the men and 4 '8 i)er cent, of the women signed the 
marriage-register with marks, instead of with their names. 

In the country as a whole, the number of men unable to write 
is considerably less than that of Avomen, though the difference 
betAveen the tAvo sexes is rapidly diminishing. Taking the 
counties separately there is great discrepancy, the general rule 
being that in agricultural counties (particularly the southern) the 
male, and in mining and industrial counties (particularly the 
northern) the female, is the Avorst educated sex. 

In the northern part of the country the amount of illiteracy is 
much greater for each sex than in the southern part. 



CHAPTEE VIII. 



FECUNDITY OF MARRIAGE. 



MAERIAGE being the great institution by which the popula- 
tion is chiefly regulated, it becomes necessary to consider 
the conditions regulating the fertility of marriage. The two 
most important of these are the duration of married life, and 
the age at which marriage is contracted by women, Avhich are to 
a large extent mutually inter-dependent. 

From the English census 1891, the number of wives under 
forty-five years of age can be ascertained. Comparing these with 
the number of legitimate births in the three years 1890-92, the 
average annual fecundity of wives of reproductive ages is repre- 
sented by 264 live births to 1000 wives. Similar calculations 
made from the returns of 1881 and 1871 respectively give annual 
fecundities of 286 and 292 per 1000 wives. A gradual reduction 
of fecundity is thus shoAvn. This reduction of fertility is partially 
ascribable to the lowering of the marriage-rate, Avhich is necessarily 
associated with a reduction of the proportion of neAvly-married 
women among the wives under forty-five, and partially also to the 
raising of the mean age at marriage. 

Dr. J. Bertillon* prefers the age-group 15-50 for calculating the 
legitimate birth-rate, and some of his results are here reproduced : — 





Years of 
Observation. 


Legitimate Birth-rate per 

anmim to every 1000 wives 

aged 15-50 years. 


Illegitimate Birth-rate per 

annum to every 1000 

unmarried women aged 

15-50 years. 


Including 
still-born. 


Excluding 
still-born. 


Including 
still-born. 


Excluding 
still-born. 


France 
Belgium . 
Italy 

Germany . 
Austria . 
Sweden . 
Norway . 
Denmark . 


1878-82 
do. 
do. 
do. 
do. 
do. 
do. 
do. 


173 
275 
249 
278 
250 
245 
283 
248 


166 
263 
242 
265 
244 
239 
274 
240 


17 

20 

25 
29 
46 
22 
20 
27 


16 
19 
24 
28 
44 
21 
19 
26 



cit., p. 43. 



FECUNDITY OF MAERIAGE. 



65 



Tlie. following figures are taken from the 1S90 Census Report 
of the United States (part i. on "Vital and Social Statistics," 
p. 481):— 





Birth-rate 


per 1000 of 


All Females between 15 and 50 
years of Age. 


Married Females between 15 
and 45 years of Age. 


Registration 
Area . 

Cities . . 
States . . 


Total. 


White. 


Coloured. 


Total. 


White. 


Coloured. 


85 


86 


78 


1 
184 184 


175 


88 
81 


89 

81 


77 
80 


192 193 
176 176 

i 


172 

184 



Thus tlie l)irth-rate of the coloured was less than that of the 
white, and the birth-rate of the white population was greatest in 
the cities. 

The figures in the preceding table have only an approximate 
value, being based on somewhat incomplete data. The same 
remark applie.'^. to the following table from a paper liy Dr. AVillnir 
in the Annual Report on the Vital Statistics of ^Michigan for 1894. 

The Fecundity op Marriage of Native-born and Foreign-born 
Women in Michigan, 1870-94, in five-year Periods, approxi- 
mate Corrections having been made for Imperfect Returns. 



Five-year 
Periods. 


Children born per 1000 

women between 15 and 

45 years of Age. 


Children born per 
marriage, with mother. 


1870-74 
1875-79 
1880-84 
1885-89 
1890-94 


Native. 


Foreign. 


Native. 


Foreign. 


124 
127 

122 
117 
111 


231 
235 
221 
227 
232 


3 8 
3-3 
3-0 
3 


6-5 
6-5 
4-9 
5-1 



The age at marriage is the chief factor controlling the propor- 
tion of children to a marriage, the age of the wife being the most 
important element, because of the fact that child-bearing is limited 



66 VITAL STATISTICS. 

practically between the sixteenth and forty-fifth years of life. The 
fathers and mothers of nearly half the children born are, according 
to Dr. Farr, under thirty years of age. 

What amount of Reduction in the Marriage-Rate would he re- 
quired to produce under present conditions a stationary pojndation ? 
Dr. Ogle has discussed this subject in detail in the Jour. Royal 
Statist. Soc, vol. liii. part ii. 

His calculations show that " in the very improbable event of all 
women retarding their marriages for five years, we should have a 
birth-rate of 23'3 per 1000," which, on the basis of the death-rate 
of 17*8 in 1888, would still leave the population growing at the 
rate of between 5 and 6 per 1000 annually. It is evident that in 
view of the fact that in the last 23 years the mean age at marriage 
of spinsters has only increased by 0"8 years, Ave may "dismiss 
altogether the notion that any adequate check to the increase of 
pojDulation is hereafter to be found in retardation of marriage." 

Similarly, if without any alteration in the age at marriage Ave 
attempt to secure a stationary population by simple decrease of 
the marriage-rate, we have, taking the figures of 1888, to inqiiire 
what marriage-rate corresponds to the legitimate birth-rate of 16*4 
in that year. The average number of children to a marriage being 

16"4 
about 4"2, the marriage-rate Avould have to be = 3'9, or, ex- 

pressed according to the English method (there being tAVO parties 
to a marriage), 7 "8 per 1000, i.e., 45 per cent. beloAV the point it 
has ever yet touched. 

HoAv if both methods are combined? It can easily be calculated 
that Avith an average of 3-1 children to a marriage, resulting from 
an average retardation of female marriage for 5 years, a marriage- 
rate of 10 '6 per 1000 Avould give a legitimate birth-rate of 16 "4, 
Avhich with 1"4 for the illegitimate birth-rate would give a total 
birth-rate of 17-8, Avhich is also the death-rate of 1888. Or as 
Dr. Ogle sums up : " If one-quarter of the Avomen Avho now marry 
were to remain permanently celibate, and the remaining three- 
quarters Avere to retard their marriages for five years, the birth- 
rate would be reduced to the level of the present death-rate." 

Age in Relation to Fecundity. M. Korosi (Budapesth)* has 
drawn up tables of natality {Philos. Trans., 1893) analogous to 

* A Study of the Laws of Increase of Population, Public Health, vol. 
viii. p. 100. 



FECUNDITY OF MARRIAGE. 67 

a lifo-table, in \v1iieli a separate statement of the probabilities 
t)f a birth is given for eacli age of bfe. If we assume the 
(hiration of fecundity in the male to be about fifty years, and 
that of the female about forty years, the question of fecundity 
can only be solved by a division into at least 2000 questions, 
since each year of age of one parent must be combined with 
each year of age of the other. Such taJ)les of natality, giving 
the probability of a birth for each combination of ages of fecundity, 
have 1)een possil)le in Budapest since LSSO, as the birth returns 
state inter alia the ages of parents, ])revious births in same family, 
etc. The census returns for 1891 gave the number of couples 
living among the same combinations of ages. From four years' 
oliservations, emliracing 40,931 births, the ratio of annual l»irths 
to 1000 marriages is found to be 16.3. I»ut many of the total 
marriages having passed the period of proliticity, a separate 
statement must be given for each year of life. Kcirosi gives his 
results both mono-sexually and bi-sexually. Stating them rnono- 
se'jnially they show that the fecundity of the female in Buda])est 
reaches its maximum between the 18th and 19th year, descending- 
then in a regular line to the age of 45-50, Avhen it ceases. 
Every hundred marriages of girls under eighteen years of age 
only produce within a year 36-38 infants. From 18-20 years, 
fecundity reaches its maximum of 40 per cent., i.e., 40 children 
within a year. At 25 years, it is 32 per cent ; at 30 years, it is 
24 per cent; at 35 years, 17 per cent; at 40 years, scarcely 
7 ])er cent; at 50 years, 0-1 per cent. 

^len attain the maximum of their fecundit}'' at 25-26 years, 
when it is 35 per cent ; at 35 years it has fallen to 23 per cent. ; 
at 45, to 9-5 per cent. ; at 55, to 2-2 per cent. ; and at 65, to 0-5 
jier cent. The figures relate to effective, and not to physiological 
fecundity. Prudential considerations frequently come into opera- 
tion in later married life, as clearly shown by the following 
figures : — ■ 

Fecundity of Marriage at Various Age-Groups. 



-Age. 


Fur Women 
newly-inaiTied. 


For all Women. 


30-34 years. 
3.5-39 „ 
40-44 ,, 


32-9% 
32-7% 
21-4% 


20-6% 

14-7% 
5"9% 



68 



VITAL STATISTICS. 



Stating the results hi-sexuaUy, i.e., according to the change 
of age in both parents, the following results are obtained. For 
100 females of the following ages, the probability of a birth 
occurring in a year varies with the age of the man as follows : — 



Age of Father. 


Age of Mother. 




25 years. 


30 years. 


35 years. 


25-29 years. 


35-6% 


25-0% 


21-2% 


30-34 ,, 


31-2% 


23-6% 


19-9% 


35-39 „ 


27-5% 


21-8% 


19-4% 


40-44 ,, 




16-7% 


14-0% 


45-49 ., 


— 


14-4% 


10-9% 


50-54 ,, 


— 


— 


10-9% 



On the other hand, the fecundity of the fathers varies as follows 
with the age of the mothers : — 



Age of Mother. 


Age of Father. 




25 years. 


35 years. 


45 years. 


55 years. 


Under 20 years. 


49-1% 


— 


— 


— 


20-24 „ 


43-0% 


31-3% 


16-0% 


— 


25-29 ,, 


30-8% 


27-3% 


18-5% 


— 


30-34 ,, 


33-5% 


23-7% 


14-4% 


8-1% 


35-39 ,, 




18-9% 


11-8% 


6-7% 


40-44 ,, 


— 


6-6% 


6-1% 


3-0% 



M. Korosi anticipates that these probabilities of birth may in 
time be practically utilised in the same way as the probabilities 
of mortality tables. The latter are the basis of life assurance, 
the former may furnish the basis of a new branch of assurance. 

The same tables answer the question as to the appropriate age 
of the female to secure the greatest fecundity. Thus a man aged 
25 years ought, from this standpoint, to choose a wife aged 19 years; 
a man aged 35 a wife aged 21 years ; at 40 years a wife of 24 ; at 
45 a wife of 29 years old. 

In a contribution to the Eoyal Society on M. Kbrosi's tables, 
Mr. Francis Galton has made an ingenious attempt to reduce 
to a single formula the probability of births for numerous com- 
binations of ages, and made further combinations of ages of the 
same fecundity, establishing between them similar connections to 
those seen in geographical maps for places of the same temperature 



FECUNDITY OF .AIARRIAGE. 



69 



and altitude. These lines, analogous to isotlienns and isobars, are 
described as isogenes. 

Duration of Married Life. Instating numerically the fecundity 
of marriage, the (|uestion arises as to what marriages shall be 
comi)ared with the births of a given year. If we could follow 
the families and count all the children resulting from a given 
-marriage to the end, the fecundity of the marriage would be 
accurately represented. If the annual marriages in a given 
community did not increase or decrease in number through a 
series of years, the division of the annual births by the annual 
marriages of the same years would express the fecundity ; but 
when the marriages are rapidly increasing, an approximation to 
the fecundity can only be obtained by dividing the births by 
the marriages of some earlier year. The year to be selected 
is determined by the interval between the mean age at marriage 
and the mean age of mothers when their children are born ; 
there are no data as to this interval in England. In Sweden 
it is 5-9 years. According to the New Zealand Year-bookp1r§94, 
it was in that country only 3'14 years in ISSl, 3 "So years in 1886, 
and 3 "62 years in 1891. 

The following table from the Registrar -GeneraVs Fortieth 
Annual Report gives the comparative fecundity of various European 
States. During the three years 1876-79 the average number 
of births to a marriage in England was 4*57. 

Comparative Fecundity in Different European States. 



Years. 


European States. 


Births to a Marriage. 


1876 


Italy . 


5-15 


J J 


Prussia . 


4-92 




Sweden . 


4-84 




Netherlands . 


4-83 




England 


4-63 




Belgium 


4-48 


1870 


Spain . 


4-47 


1876 


Denmark 


4-24 


)) 


Austria . 


3-73 




France . 


3-42 



Assuming that the interval between the mean age of marriage 
and the mean age of mothers in England is six years, as in Sweden, 



70 



VITAL STATISTICS. 



then the legithnate births in 1874 divided by the average number 
of marriages in the three years 1867-9 will give the average 
number of births to a marriage, which was 4'57. In 1864 it 
was 4'30, but the apparent increase is probably owing to improved 
registration of births. 

The corresponding figures for Michigan are given on p. 65. 

The following figures are quoted by Dr. Wilbur* from the 
Victorian Year Book, 1894, p. 300. It is probable that the results 
have been obtained by various methods. They can therefore only 
be regarded as possessing an approximate value. 



Children to a Marriage in various Countries. 





Children 




Children 


Country. 


to each 


Country. 


to each 




marriage. 




marriage. 


Russia in Europe (1888) 


5-7 


Italy .... 


4-6 


Ireland 


5-5 


Scotland 








4-4 


New Zealand 


5-2 


Holland 








4-3 


Finland (1887) . 


50 


Victoria 








4-2 


I Russian Poland (1888) . 


4-9 


Belgium 








4-2 


Western Australia 


4-8 


England 








4-2 


Tasmania 


4-7 


Sweden 








4-0 


New South Wales 


4-7 


Denmark 








3-6 


South Australia . 


4-7 


Japan (1888-91) 




3-5 


Queensland . 


4-6 


France 




3-0 



In jSTew South Wales the age at marriage, together with the 
number of children she has borne, is registered in connection with 
tire record of the death of each female. In the year 1893, the 
mean number of children borne by women married at 15-19 years 
of age inclusive is 6*76. From 20-24 inclusive it is 5 '32, a loss 
of 1"44 children per marriage attending an advance of five years 
in age at marriage. 

* Op. ciL, p. 119. 



CHAPTER IX. 

BIRTHS. 

THE consideration in the last chapter of marriages and their 
average fecundity naturally opens the way to a discussion of 
birth statistics. Such statistics are of value in giving information 
as to the rate of natural increase of the population, and the age 
and sex-distribution of the population, in addition to their great 
social interest, especially when the statistics of illegitimacy are 
included. 

Estimation of Birth-rate. The birth-rate may be estimated 
by the following plans, of which the third is the most accurate, 
though not so easily available for ordinary purposes. (1) The 
birth-rate is reckoned as a rate per 1000 of the population living at 
all ages, in the middle of the year. This may be described as a 
crude birth-rate. It is fairly satisfactory when used for the same 
community in a series of years, or in comparing the birth-rates 
of communities whose populations are known to l)e nearly, if not 
quite, identical in their age and sex-composition. If, however, 
the number of women living at child-bearing years differs in two 
populations, the birth-rate per 1000 of the total population would 
vary from this cause, apart altogether from varying fecundity of 
the two populations. 

We may (2) calculate the proportion which the births registered 
bear to the women living at child-bearing years — i.e. roughly 
between about 15 and 45 years of age. These are shown by the 
census returns for each urban and rural sanitary district ; and as 
the age and sex-composition, except in abnormal cases, does not 
vary greatly in an intercensal period, the same proportion of 
women aged 15-45 to the total pojnilation may be regarded as 
holding good throughout the intervening period between any two 
census enumerations. 

71 



72 



VITAL STATISTICS. 



(3) The second method would be sufficiently accurate in 
comparing two towns like Bradford and Leeds, in which the 
social and industrial conditions are presumably identical. If, 
however, an industrial parish like Whitechapel were to be com- 
pared with a fashionable district like South Kensington by either 
the first or second method given above, the results would be 
misleading. 

And, speaking generally, the only completely accurate method 
of stating the birth-rate is to subdivide the births into legitimate 
and illegitimate, stating the former per 1000 of married women 
of child-bearing years, and the latter per 1000 of unmarried 
women of child-bearing years. The relative accuracy of the two 
former methods and of the last method is shown in the following 
table : — 

Legitimate Birth-Rates in Kensington and Whitechapel. 

189L 









Percentage 








excess of birth- 




Kensington. 


Whitechapel. 


rate in White- 
chapel over 

that in 
Kensington. 


A. Birth-rate per 1000 inhabi- 








tants .... 


21-8 


39-9 


83% 


B. Birth-rate per 1000 women 








aged 15-45 years 


61-6 


172-1 


177% 


C. Birth-rate per 1000 married 








women aged 15-45 years . 


215-4 


3-28 -3 


53% 



The social condition of Kensington imiolies a large proportion of 
female unmarried servants, who contribute but little to the birth- 
rate. Among married women of the child-bearing age the true 
birth-rate is 53 per cent, higher in Whitechapel than in Ken- 
sington (C). The statement of the birth-rate by the ordinary 
method (A) exaggerates the true difference to the extent of 30 per 
cent., while its statement by the second method (B) exaggerates it 
to the extent of 124 per cent. 

A tabulation of the comparative illegitimate birth-rates for the 
two above districts will complete our illustration of the methods 
of statement of birth-rate. 



BIRTHS. 



73 



Illegitimate Birth-Rates in Kensington 


AND WhITE( 


:;hapel, 1891. 




Kensington. 


Whilcchapel. 


Percentage 
excess of illegi- 
timate birtli- 
rateof Wlilt«- 
chapel over 

that of 
Kensington. 


A. Biith-iatc per 1000 inhabi- 

tants .... 

B. llirtli-iato per 1000 women 

aged 15-45 years 

C. Birth-rate per 1000 unmarried 

women aged 15-45 years 


1-19 
3-35 

4-68 


1-26 

5-44 

11-43 


6% 

62% 

136% 



Thus a statement of the illegitimate birth-rate in terms of the 
entire population gives the completely erroneous impression that 
illegitimacy is nearly equal in amount in Kensington and White - 
cha})el. A statement in proportion to the total number of women 
aged 15-45 only shows an excess of 62 per cent, in the latter; 
while a statement in proportion to the number of unmarried 
women at child-bearing ages shows that it is nearly two and a half 
times as high in Whitechapel as in Kensington (excess of 136 per 
cent.). 

Defects in Registration of Births. I'rior to the operation of 
tlie Civil Registration Act of 1837 there were no trustworthy 
birth statistics. In the earlier years of the operation of the Act 
registration of births was undoubtedly defective, Dr. Farr esti- 
mating the deficiency during the 39^ years ending Avith 1876 at 
5 per cent. The registration of births was first made compulsory 
by the Births and Deaths Registration Act of 1874 ; and it is 
probable that at the present time tlie failure of registration is 
very small, and chiefly confined to illegitimate births. There are 
two grave defects in the Birth Registers of the United Kingdom. 
The ages of the mothers at the birth of each of their children are 
not stated, nor is the order of their birth recorded, so that tfie 
number of children borne by women at ditterent ages, and the 
total number in the course of their lives, cannot be ascertained in 
this country. 

National and International Birth-rates. The total English 
birth-rate, legitimate and illegitimate, averaged 32 '6 [)er 1000 of 
population in 1841-50. It reached its maximum (36"3) in 



74 



VITAL STATISTICS. 



1876, and since then has steadily declined to a minimum of 29 '6 
in 1894. In 1895 it rose to 30-4, and in 1896 it was 297. 

Tlie relationship between the crude birtli-vate and the true 
birth-rate may be gathered from the following data for the two 
census years 1881 and 1891 : — 

England and Wales. 





ISSl. 


1S91. 




Legitimate. 


Illegitimate. 


Legitimate. 


Illegitimate. 


Birth-rate per 1000 persons 
at all ages . 

Birth-rate per 1000 mar- 
ried orunmarried women 
aged 15-45 years . 


32-2 

•285-6 


1-7 
14-1 


30-1 

268-0 


]-3 
10-6 



The teaching of this table may be further elucidated by stating 
the percentage decline of each rate for 1891 when compared with 
corresjDonding rates for 1881. 

Decline per cent, op Birth-rate op England and Wales 
between 1881 and 1891. 

Legitimate. Illegitimate. 

(ft.) Of crnde birth-rate 6-5% ... 23-5% 

(6) Of accm-ately determined birth-rate . . 6"2% ... 24*8% 

The conclusions derived from the accurately determined birth- 
rate confirm in the main those derived from the crude birth-rate ; 
the differences being that the legitimate birth-rate has declined 
slightly less and the illegitimate birth-rate considerably more than 
the crude rates would indicate. 

On p. 64 will be found accurately determined birth-rates for 
some other European countries. 

The English birth-rate varies considerably in different counties, 
the lowest rates occurring in the agricultural, and the highest in 
mining and industrial districts. Thus in 1895 the lowest birth- 
rates were in Sussex (24-3), Surrey (25-0), Westmoreland (25-4) ; 
the highest in Monmouthshire (35-0), Staffordshire (35-6), and 
Durham (35-8). 

The higher birth-rate in urban populations, which are to a 
great extent included in mining and industrial districts, is OAving 
in part to the higher marriage-rate, and in part to the earlier 
marriage of women, and the greater mortality among infants, 



BIRTHS. 



75 



wliicli, by slioi'tening tlie period of suckling, diminislje.s the inter- 
vals of child-hearing, lint the chief reason is dou))tIess the fact 
that in ui'Ikui populations there is a greater proportion oi Avonien 
at cliild-l)eai'ing ages. 

In the thirty-three great towns the Itirth-rate in liS07 averaged 
30"7 i>er 1000 inhabitants, varying from 22'5 in Halifax, 23-4 in 
lluddersfield, and 24-G in Bradford, to 35*1 in Salford, 35-3 in 
Liverpool, and 35'8 in (lateshead. The dilierences between the 
crude Ijirth-ratcs of these towns represent in part real ditferences of 
fecundity ; in part, diiferences of a social and industrial character, 
causing diilerences in the proportion of the total population who are 
niarri(!d women of cliild-l)earing age. The proportional share of 
these factors can only ]je shown by a system of correction, of which 
I have already given two examples ([jp. 72 and 73). 

Social Position has a considerable influence on the birth-rate, 
though tliere are very few accurate data on this point. The 
fallacy involved in the fact that people's social position tends 
to inij)rove as their ages advance should be remembered. We 
liave already seen ([>. Gl) that persons of the higher classes marry 
at a later age than others. There are, as Ave have also seen, 
serious fallacies involved in comi)aring the crude birth-rate of 
two jiopulations. The following further instance may be given : 
The late Sir E. Chadwick compared the metropolitan births, 
which at the time of his remarks were 1 in 37 of the population, 
with those of Herefordshire, Avhich were 1 in 44 ; but Mr. 
Neison shoAVcd that this difference was largely explained by the 
fact that while the population aged twenty to forty was 36*33 per 
cent, of the total population in London, it was only 28"39 
l)er cent, of the total population in Herefordshire. Dr. J. 
Bertilion, at tlie meeting of the International Statistical Institute 
at St. Petersburg, September, 1897, gave the following statistics 
as to the births ])er 1000 women aged fifteen to fifty per annum 
in different quarters of the under-noted cities : — 



Classilication. 


Paris. 


Berlin. 


Vienna. 


London. 


Very poor quarters 
Poor quarters 
Comfoi'table quarters 
Very comfortable quarters 
Ricli quarters 
Very rich quartei-s 


108 
95 
72 
65 
53 
34 


157 

129 

114 

96 

63 

47 


200 
164 
155 
153 
107 
71 


147 
140 
107 
107 
87 
63 


Average 


80 


102 


153 


109 



76 



VITAL STATISTICS. 



Probably the birth-rate is really higher among the poor than 
the rich, but the preceding figures cannot be entirely trusted — at 
least, so far as London is concerned. They require to be checked 
by calculation of the legitimate birth-rate per 1000 married women 
at child-bearing age in each district (see p. 72). 

The influence of National Prosperity on the birth-rate is in 
the same direction as its influence on the marriage-rate (pp. 59 
and 60). 

The birth-rate in England varies slightly according to season. 
In the first quarter of 1893 the English birth-rate was 31 "5, 
in the second, 31 "7, in the third, 30"6, and in the fourth, 29*2 per 
1000 of the population. The data for ascertaining the four- 
weekly birth-rate in London are given on p. liii. of the Annual 
Summary of Births, Deaths, etc., 1897. 

In the Statistisches Jahrhuch for Berlin, 1895, the following 
table is given : — 

The average Daily Number of Births for each Calendar Month 
STATED IN Proportion to the average Daily Number for the 
Whole Year = 100. 





Live-Born. 


Still-Born. 


Total. 


January 
February 
March . 
April 
May 
June 
July . 
August . 
September 
October . 
November 
December 






105-4 

104 7 

104-5 

98-1 

100-5 

101-6 

103-1 

101-8 

101-4 

95-5 

90-1 

93-3 


99-5 

112-9 

110-3 

110-5 

107-2 

96-4 

89-2 

97-9 

101-0 

88-1 

89-7 

87-3 


104-6 

105-9 

105-4 

99 9 

101-5 

100-8 

101-1 

101-3 

101-3 

94-4 

90-0 

93-8 








100-0 


100-0 


100-0 



The following details from the Bericht des Medicinalrathes 
ilber die Medicinische Statistik des Hamhurgischen Staates, 1896, 
may be added, especially as no such data as to still -births 
are possible under the present system of registration in the 
English Registrar-General's reports : — 



BIRTHS. 

City of Hamburg — Monthly Births. 



77 





Percentage of Total Annual 
Births occurring in each Month. 


Percentage occurring in each 
Month of 1S96, of 


1 
Mean of ; , „„. 
1S81-90. 1 ^^^^• 


Live Births. 


Still Births. 


January 
February . 
March 
April 
May 
June 
July 
August 
Septem])er . 
Octolier 
November . 
December . 


8-2 
8-G 
8-7 
8-3 
8-3 
8-1 
8-2 
8-3 
8-5 
8-3 
8-2 
8-3 


8-2 
8-6 
8-7 
8-2 
8-1 
8-2 
8-2 
8-2 
8-6 
8-2 
8-5 
8-3 


8 3 
8-6 
8-6 
8-0 
8-1 
8-1 
8-4 
8-3 
8-8 
8-2 
8-5 
8-1 


7-9 
9-1 
9-4 
9-6 

7-4 
8-7 
7-0 
7-4 
7-6 
8-5 
7 "7 
9-7 


100-0 


100-0 


100-0 


100-0 



The Berlin and Hamburg returns are interesting, as showing that, 
with one exception (December in Hamluirg), the highest proportion 
of still-births in both cities occurs in the months of February, 
March, and April. The three months in which the highest pro- 
portion of live-births occurs are January, February, and March in 
Berlin, and September, February, and March in Hamburg. 

The influence of Nationality is shown in Fig. 4. The com- 
parative birth-rates for twelve European countries, as well as the 
constituent parts of the United Kingdom, are given in the 
English Registrar-General's rejDorts (1896, pp. cxv.-cxxxii.), the 
li:>ngest annual series being that for Sweden, which dates back to 
18-51. There has been a general decline in the l^irth-ratc, though 
this is much more marked in some countries than in others. This 
decline has almost ceased in the last two years. 

Causes of Decline in Birth-Rate. The explanation of the 
steadily declining birth-rate must be sought in some cause or 
causes which are in operation throughout the civilized world, as 
the phenomenon is a general one. The greater extent of the 
decline in the birth-rate in certain countries will help in deter- 
mining the chief operating causes. The two in which the decline 
is apparently the greatest are France and Massachusetts. Of the 



1 8 3 4 5 6 7 8 9 10 11: 12 13 14 15 16 17 18.19 20 21 22 23 24 25 2G 27 28 29 




-- Hungarj" 



-I — Austria 

German 
■ [ Empire 



E. & 

iWales 
Scotland 
Belgium 
""Switzerland 

enmark 



Ireland 
France 



Illegitimate 
"i birth-rate 
Berlin 
England 



Fig. 4.— Birth-rates, 1871-95, in different European countries. 



BIRTHS. 79 

latter Mr. Dike, quoted by Dr. Willnir,* says: "The declining 
fruitfulnoss of the family, especially among peojile of the so- 
called native stock, has l)ecome a matter of serious concern. In 
Massachusetts, the mother of foreign hirtli has on an average 50 
per cent, more children than the mother born in this country. 
]<'' ranee is the only country in Europe whose birth-rate is as low as 
that of -Massachusetts, and France is alarmed at her condition. 
Massachusetts is indifi'erent, for she can recruit her population 
fi'om Ireland and Canada." 

It will have lieen seen from previous remarks (p. 66) that 
(a) Postj)onement of marriage to more mature years, and (b) 
a larger projiortion of celil»acy, only account for a share of the 
decreased Ijirth-rate. 

((') The greater ease Avith which divoi'ce is obtained in non- 
Roman Catholic countries has a certain amount of influence, 
especially as many of the divorces occur at child-bearing ages, and 
the divorced often do not re-marry. The mean duration vof married 
life was calculated by Farr in 1871 to be 27 years. Dr. Wilbur 
states that the mean duration of marriages interrupted by divorce 
in Michigan is less than 10 years. 

(d) There is no reasonable ground for the view that a diminished 
power of either sex to produce children has been produced by 
alcohol, syphilis, tobacco, or other causes. 

(e) It is quite clear that the main cause of the diminution in 
the birth-rate is " the deliberate and voluntary avoidance of child- 
bearing on the part of a steadily increasing number of married 
people, who not only prefer to have but few children, but who 
know how to obtain their wish."! That this is the chief reason 
is shown by the extremely high birth-rate among the French 
population in Canada, and the abnormally low birth - rate in 
France. The difference is inexplicable on the score of climate, 
or indeed of any other known cause, except that the former who 
are orthodox Roman Catholics are prohibited by their religious 
beliefs from practising the artificial means of preventing lai'ge 
families which find favour in France. 

Still -births are not registered in England; but under the 
Registration Act no still-born child can be buried without a 
certificate from a registered practitioner in attendance, or from 
one who had examined the body, or in his absence a declaration 
from a midwife or some other person qualified to give the informa- 

• Op. cit., p. 125. 

t Paper by Dr. J. S. Billings, Foricm, Dec, 1849. 



80 



VITAL STATISTICS. 



tion to the effect that the child was still-born. The proportion of 
still-births to total births in this country is supposed to be about 
4 per cent.; but this is uncertain. In France and Belgium the 
children dying either before or after birth, if they die before 
registration, are recorded as still-born. This fact should be re- 
membered in estimating the true death-rate and birth-rate of 
France. Thus the corrected death-rate of France in 1875 becomes 
23*4, instead of 23"1, per 1000 of population {Registrar-GeneraV s 
Thirty-eightli Annual Report). In Italy, Germany, and in the four 
Scandinavian countries, the term " still-born " is used in the medico- 
legal sense.* The proper plan would be to register all still-births 
in a separate category, distinct from both births and deaths. The 
males outnumber females in still-births, probably owing to greater 
difficulty in child-birth. Thus, in the ten years 1865-187.5, they 
were in France, 144; Italy, 140; Belgiinn, 135; Sweden, 133; 
and in Prussia 129 to every 100 female still-births. 

In Berlin in 1895 the proportion of males to females among 
the still-born was 137 to 100, among the live-born 104 to 100. 
In Hamburg in 1896 the proportion of males to females among 
the still-born was 125 to 100, among the live-born 107 to 100. 
(See also p. 24.) 

The proportion of still-born is greater among male illegitimate 
than among male legitimate children. This is clearly shown by 
the following figures f : — 







Of every 1000 births, including 


Country. 


Period of 


still-born, the number of still- 


Observation. 


born, or declared as such, was as 






follovfs among — 






Legitimate. 


Illegitimate. 


(1) Coun 


tries in which inquii'y as to 




paternity is forliddcn. 


France .... 


1878-82 42 78 


Belgium .... 


do. 43 58 




(2) Countries in which ioiquiry as to 




paternity is alloiued. 


Prussia .... 


1878-82 


39 


54 


Austria .... 


do. 


24 


38 


Hungary . 


do. 


14 


30 


Sweden .... 


do. 


28 


37 


Norway .... 


do. 


32 


50 



* i.e., a viable infant (having had over six months of intra-uterine life, or 
being twenty-five centimetres long) which is dead without having breathed, 
t Bertillon, op. cit., p. 59. 



BIRTHS. 



81 



Proportion of Males and Females at Birth. In 1838-47 the 
males l)orn to every 1000 females liorn averaged 1050. Since 
then the proportion has gradually declined to 10.3G in 1891-95. 
(See tables 3 and 4, Fift ij-ei(jliili Animal Report of the Registrar- 
General, 1895.) In registration counties the lowest proportions 
of male to female births were 974 per 1000 in Cumberland, 981 in 
Oxfordshire, and 988 in Derbyshire; the highest 1083 per 1000 in 
Dorsetshire, 1101 in Huntingdonshire, and 1188 in Rutlandshire. 

In Berlin in 1895 the proportion of male to female births was 
1047 per 1000; in Hamburg it was 1075 in the same year, 
having increased fairly steadily from 1885, when it was 1032. 
In previous years the proportion of male births to 1000 female 
births was higher than this; thus in 1883 it was 1080. In 
London, on the other hand, the proportion has remained fairly 
constant, and is lower than in the continental cities; it was 1041 
in 1880 and 1036 in 1895. 

The [)roportion of boys to girls at l^irtli is smaller in England 
than in any European country, and for some unexplaineil reason 
the excess in the proportional number of boj^s is gradually de- 
clining. The proportion of males is greater in large than in 
small families ; it is also greater among the earlier born than 
among the later born infants in a family. According to Bertillon, 
the last rule does not apply to illegitimate l)irths. 

It is interesting to compare the proportion of the two sexes 
as shown l^y the census returns and by life-table experience. 
The following table gives the proportion of males and females 
at each age-group at the census 1891 : — 

In England and Wales there were at the Census 1891 the 

FOLLOWING NUMBER OF MaLES TO EVERY 1000 FeMALES 
at EACH AgE-GROUP. 



All Ages 



Propoition of Males 
to 1000 Females. 
940 



0- . 


985 


1- . 


988 


2- . 


993 


3- . 


990 


4- . 


993 



Under 5 years 
5- . ■ . 
10- . 
15- . 
20- . 

G 



989 
996 
999 
985 
891 



Ages. 

25- . 
30- . 
35- . 
40- . 
45- . 
50- . 
55- . 
60- . 
6.5- . 
70- . 
75 and ( 
upwards ( 



Proportion of Males 
to 1000 Females. 
896 
931 
945 
931 
924 
901 
877 
858 
832 
795 

732 



Males. 


Females. 


509,180 


490,820 


427,184 


426,461 


402,706 


403,980 


393,110 


394,689 


387,062 


388,716 


382,646 


384,432 



82 VITAL STATISTICS. 

The results in this table, based on the population as enumerated 
in 1891, do not correspond with the life-table experience based 
on the mortality in England and Wales in the ten years 1881-90. 
In this life-table a miilion infants, in the proportion of 509,180 
males to 490,820 females, are traced from birth through life. 

English Life-Table, 1881-90. 

^o-e. Born and Surviving at each Age (/^.). 

. . . 

1 . . . 

2 . . . 

3 . . . 

4 . . . 

5 . . . 

Thus, although at birth the million infants comprise an excess 
of males, before the end of the second year of life the balance is 
more than restored, females being in excess. 

If, instead of starting in the life-table with males and females 
in the proportion shoAvn by the birth-returns, we take a million of 
each sex, then according to the English experience in 1881-90 
the males will have been reduced to one-half of their original 
number between the 51st and 52nd year of life, the females 
between the 56th and 57th year of life. The differences between 
the life-table results and the census figures are partially explicable 
on the ground of errors in the census returns; but are chiefly 
caused by the higher death-rate and the greater migration among 
males. 

Illegitimacy. Illegitimacy has important bearings on social 
problems, as well as on the chances of life of infants, and there- 
fore deserves careful consideration. 

It may be stated, (1) like the total birth-rate, as a proportion 
to every 1000 of the population. 

(2) The most accurate method is to state it as a proportion to 
the number of unmarried women living at child-bearing ages. 
(See p. 72.) 

(3) It is often stated as a proportion to the total births. This 
method is fallacious, as the number of legitimate births varies 
with the marriage-rate, and this with the activity of trade; so 
that if the marriage-rate were low, and the number of illegitimate 
births remained stationary, the amount of illegitimacy Avould 
appear larger than usual, when not really so. 



BIRTHS. 83 

Illegitimacy in England. The number of illcgitiinate births 
per 1000 of popuhiticiii has varied from a maximum of 2'3 in 
LS50-52, in 1859 ami in 1863-64, to a minimum of 1*3 in each 
of the years 1890-95. (See tables 3 and 4, pp. xxxviii. and xh 
Jie(/ififrar-Ge7ieral't< Beport, 1895.) 

Tlius the illegitimate birth-rate has declined along \vitli the; 
decline in the marriage-rate and in the legitimate birth-rate. The 
talile on p. 74 shows how far this comi)arison may be trusted, and 
inilicates that the reduction in the illegitimate birth-rate between 
1881 and 1891 was four times as great as the reduction in the 
legitimate birth-rate. 

For similar reasons it is iloubtful how far the comi)arison 
between the amount of illegitimacy in the diii'erent counties of 
England is trustworthy. Stated as a proportion of illegitimate to 
legitimate births, the ratio was lowest in iSIiddlesex and Essex in 
1895 (29 per 1000), in Monmouthshire (31), South AVales (33), 
and highest in North Wales (65), Cund)erland (70), Herefordshire 
(72), and Shropshire (74). 

It is a remarkable fact that altlioiigh the mean age at marriage 
has increased, antl the i)roportion of marriages under age has 
tlecreased, the illegitimate birth-rate has likewise decreased. 

Illegitimacy in other Countries, The table on p. 64 gives 

interesting details on this point. The difference in definition of 
still-lnrths in various countries (p. 80) must be borne in mind. 

Judged by the proportion of illegitimate births to population, 
illegitimacy is much greater in amount in Berlin than in P]ngland 
(see Fig. 4). In 1892-95 the annual illegitimate births averaged 
4"2 per 1000 of the population, as compared with 1*3 in England 
as a whole. A usefid comparison may be made between the data 
in the tables on pp. 64 and 74. Tlie illegitimate birtli-rate in 
England and Wales is stated in terms of the unmarried women 
aged 15-45, that for other countries in terms of the larger group 
comprised by unmarried women aged 15-50. Notwithstanding 
tliis fact, England stands lowest on the list, having only one-fourtli 
of the amount of illegitimacy of Austria, which occupies the highest 
position on the list. 

The Malthusian Hypothesis. It has not been thought 
necessary to reproduce the account and criticism of Malthus' 
K^xaij on Poj'uJafion (1798) wliich appeared in former editions 
of this work. The reader wishing to study the subject will iind 



84 VITAL STATISTICS. 

it fully discussed from different standpoints in the following 
works : — 

Sitppleinent to the TMrty- fifth Annual Reiport of the Registrar-General 

(Farr, pp. xv.-xx.). 
Character and Logical Method of Political Economy (J. E. Cairnes, ll.d. 

Chapter on Maltliusianism. Second Edition, 1875). 
Populcdion and Capital (G. K. Rickards, m.a. , 1854). 
On Population (William Godwin, 1820). 
Economic Stiidies (W. Bagehot, 1880). 
Progress and Poverty (Henry George). 
The Principles of Population and Their Connection with Human 

Hapirtness (A. Alison. 2 vols., 1840). 

It may suffice to say here that the problem of increase of 
population is not urgent, that the forecasts of Malthus and his 
adherents have hitherto not been realized, and that, although 
in a few centuries the possibilities of emigration must cease, 
assuming the same rate of increase of population as at present, 
this need excite no apprehension in view of the international 
decline of the birth-rate shown in Fig. 4. In France, and to 
a less extent in the United States, the failure of the population to 
grow by natural increase is beginning to cause some apprehension. 
(See also pp. 17 and 77.) 

Natural Increase of Population. The nahiral increment of 
a population in any year equals the births mimis the deaths. It 
may be greater, owing either to a diminished number of deaths or 
an increased niimlier of births. The actual increment is governed 
also by the balance between immigration and emigration. The 
approximate amount of emigration from the United Kingdom for 
a series of years can be seen in Table 32, p. xcviii. liegidrar- 
GeneraVs Report, 1895. 

The population of England and Wales in 1891, as determined 
by natural increment only, was 29,603,913, as actually enumerated 
29,002,525, the difference of 601,388 representing the loss by 
excess of emigration over immigration. The relationship between 
natural and actual increment in England can be studied in the 
table on p. 9. 



CHAPTER X. 

DEAT11-KATE8. 

MORTALITY statistics sui[)ass all otliur vital statistics in 
iiiiportaiice, whether they aru Cdiisidcred from a social or 
actuarial staiulpoiut, or from the standpoint of preventive medi- 
cine. 

Estimation of Death-rate. The death-rate may he reckoned 
(1) in proijortion to every thousand of the mean population ; 
or (2) the proportion of deaths, taken as unity, to the whole 
population may be stated. Thus, in 1886 the death-rate pei' 
1000 was 19-3, which is equivalent to 1 in 51. 

The two are easily convertihle by division. 

1000_ 1000 

51 -A^*^- 19-3~^^- 

The assumption underlying problems of life contingencies is, 
that the deaths in each year of age are uniformly distril)uted 
throughout the year. This assumption introduces an error ; but 
the error, except for the first years of life, is infinitesimal, 
and in all practical calculations may be disregarded. The ratio 
between deaths and po])ulation is known as the deatli-rate or rate 
of . mortality, having been so called by Farr. By actuaries, 
however, it is known as the central deafh-rate, the name rate 
of viortalitij being reserved for the probability of dying in one 
year, q^ (p. 258). 

Death-rates for Short Periods. An annual death-rate per 
1000 implies the numlter of deaths that occur among 1000 
persons, each supposed to live through a complete year of life. 
The death-rates for shorter periods are calculated on the 
assumption that the deaths would have continued in the same 
proportion during the remainder of the year. It is evident 

85 



86 VITAL STATISTICS. 

that the shorter the period to which a death-rate refers the 
greater the liabiKty to error, owing to accidental causes of 
variation. The death-rate for a short period expresses a fact, 
the errors only arising Avhcn we draw too wide inferences from 
it. Large fluctuations from accidental causes occur, especially in 
connection Avith small populations. A temporarily high death-rate 
may, for instance, only mean that, owing to the prevalence of in- 
clement weather, a considerable number of unstable and fragile 
lives have had their deaths slightly hastened. 

The death-rates for each loeelc in thirty-three great towns pub- 
lished by the Registrar-General are annual death-rates per 1000 
of the mean population of the year; i.e., they represent the 
number who would die per 1000 of the population, supposing the 
same proportion of deaths to population held good throughout the 
year. They are of service in contrasting with the death-rate of 
the same place at the corresponding period of a preceding year, 
and as showing the influence of seasonal variations ; but should 
be received with caution when used to compare one town with 
another. 

The death-rate for a week might be obtained, if there were 
exactly 52 weeks in a year, by multiplying the deaths by 52, or 
dividing the population by 52, and then proceeding as for an 
annual death-rate. But the correct number of days in a natural 
year is 365"24226, and the correct number of weeks therefore 
52-17747. The Registrar-General therefore divides, for the pur- 
poses of his weekly returns, the estimated population of each 
town by 52 "17747, thus obtaining what may be called the weekly 
population of the toAvn. Thus, if the population of a town is 
143,956, its weekly population is 

143,956 



52-17747 



= 2758, 



which is assumed to remain constant for the year for Avhich the 
calculation is required. Now, if there are 35 deaths in one week, 
then the annual death-rate for the week in question 

35 X 1000 



2758 



12-69 



It would be more logical to midtiply the deaths of each Aveek 
by 52-17747 than to deal AAdth the popidation ; but as this Avould 
require to be done each AA^eek, the former method is evidently less 
laborious, and produces the same results. 



DKATll-UATKS. H7 

The Registrar-General makes liis death-rates for each (/uarler 
refer to the thirteen weeks most nearly eorresi)on(linf,' with the 
natural (juarter; and the ([uarterly population is olitaincd hy 
niultiplyiiijf Ity thirteen the population of on(! week. 

The death-rate, expressing tiie proptjrtion home by deaths from 
all causes to eacli thousand of tlic pf)])ulation, is known as the 
general or crude death-rate. Tin; fallacies detiacting from its 
value as a test of relative vitahty will he sul)se(piently C(jnsid(;red. 
It should he regarded as the lirst test, to Vk; followed up by 
further research. It is doubtful, however, whethei', in the case of 
large populations, any more trustworthy test is available ; and its 
value may be regarded as remaining unimpaired, in spite of 
numerous attacks upon it.* 

Special Death-rates are also employed; and tlicse may be 
divided into two kinds: (1) those which dillerentiate the persons 
afl'ected as to age and sex, race, social condition, occupation, 
density of population, locality, season, etc. ; and (2) those which 
differentiate the causes of mortality, as the individual zymotic 
diseases, i)hthisis, violence, suicide, etc. 

We shall discuss in this chapter the iniluence on the death-rate 
of movements of the population, of large institutions, of the 
birth-rate, and of the age and sex distribution of the poi)ulation. 

Eflfect of Movements of Population. The effect produced by 
immigration and emigi'ation will vary in accordance with the 
average age and sex of the migrants. The mortality of most 
large and groAving towns would stand higher than it does but 

* The following weiglity cautions by Dr. C. Ivclly {Annual Report West 
Sussex, 1896) may be quoted licre : — 

" AIucli liarni has been done in jiast yeans by those who have led the inildic 
to believe too much in low death-rates, when the mere fact of a district 
having such rates ought rather to make one susjieet that some source of 
fallacy must be present. Such soiu'ccs arc to be found readily enough, and 
they are most frequent in those places which owe some of their prosperity to 
the common belief. . . . 

" It is always well to distrust a very low death-rate, and careful inquiry 
should be made into the age and sex-distribution of the population before 
coming to a conclusion. 

"In contrasting the figures year by year for tlie same district the com- 
parison may be made readily and correctly, but when other districts are 
contrasted one with the other, such a comparison may be fallacious, unless 
due allowance be made for age and sex distribution." (Sec Chap. XII.) 



88 VITAL STATISTICS. 

for the large imniljer of young and healthy immigrants from the 
country. Similarly, watering-places and residential towns appear 
somewhat healthier than they are, because of the large proportion 
of young domestic servants. 

In New Zealand the death-rate has varied from 9 '10 to 10"29 
per 1000 in the years 1887-96, a remarkably low death-rate, if 
the registration of deaths is fairly complete, for a population 
which, when enumerated in 1896, amounted to 703,360. Doubt- 
less the population is to some extent a selected one, emigrants to 
such a distant part of tlie world being usually robust and healthy. 
It might be surmised that a large share of the low death-rate of 
New Zealand is caused by the favourable age-distribution of its 
l^opulation ; but the figures do not show that this is a prominent 
factor in the case. Thus, out of every 1000 enumerated in New 
Zealand in 1896, 363 Avere aged 0-15, 583 Avere aged 15-60, and 
54 aged 60 and upwards; while in England at the census, 1891, 
the corresponding figures were 351, 576, and 73. Nor does any 
excess of children under five account for the difference between 
the Euglish and New Zealand death-rate, as in 1891 the population 
under five per 1000 at all ages was 123 in England, as compared 
with 119 in New Zealand in 1896. 

The bulk of the immigrants into towns are in good health, but 
a certain number go from the country into urban hosjoitals. 

On the other hand, many townspeople suffering from phthisis 
or other chronic disease migrate into the country, and aged persons 
very commonly do the same. 

The only Avay to avoid the fallacies arising from migration 
would be to have records kept of the niovements of population, 
and the births and deaths of each place subjected to analysis 
before comijarison is made. In order that the death-rates of 
two populations should be comparable on equal terms, so far as 
migration is concerned, it Avould be necessary that (a) the number 
of immigrants and the average duration of their residence should 
balance the number of emigrants and the average duration of 
their absence ; and that (h) the proportion of persons of each 
sex living at each age, their state of health and liability to 
disease, should be the same among both. 

Such conditions are not attainable even in European States, 
Avhere a record of migrants is kept, and much less so in this 
country ; and it is satisfactory to remember, therefore, that in 
most instances the sources of mistake tend to counteract each 
other ; and that the most important fallacy, that arising from 



DEATH-RATES. 89 

varying age-distriljuliou dt' tlic [lojiulation, can Ijc avoided by 
giving the death-rate separately for dili'erent grou}).s of ages. 

It is conuiionly assumed tliat mortality statistics may be 
ailected by migration in another way. This may be made clear 
by an exami)le. The high mortality of certain thickly-poi>ulated 
districts Avas, a quarter of a century ago, exjjlaincd as being due 
in part to the fact that, owing to the migration occurring among 
the labourhig-class population of these districts, the same house 
may in one year re])resent the accidents, deaths, and diseases of 
say twenty-four persons, instead of the six ])ersons which the 
census gives for each house. This assumi)tion was, however, 
erroneous, for, although the families occui)ying a single house 
change four times in a year, the eli'ecL of four families in excess 
of that })roduced by one family during a whole year is counter- 
balanced by the fact that it is only operating for one-fourth of 
the time. Thus, four families occuj)ying a house for three 
months each will produce the same eliect upon the death-rate as 
one family living in the "same house for a whole year, assuming 
that the numbers in the separate families, their age-constitution, 
and other conditions of life are identical. 

Brighton may be quoted as an instance of a town whose 
])opulatiou is, during the greater part of the year, swollen by 
the ingress (jf thousands of visitors, of whose number there is 
no trustworthy estimate, and who yet furnish a considcral)le 
quota to its mortality. The census enumerations in April, 1881 
and 1891 (which form the basis of calculation of the po})ulation 
for the current year), necessarily' included all the visitors present 
at those dates. There is, however, probably no time of year in 
which the number of visitors in Brighton is at so low an ebb as 
in April (when the national census is taken). 

The course theoretically least open to olyection is to exclude 
the estimated population of visitors and all deaths of visitors in 
calculating the true death-rate of Brighton. This is, unfortu- 
nately, inqu'acticable, both as regards i)opulation and deaths, and 
the death-rate is, therefore, calculated on a population smaller than 
that from which the deaths are derived. 

Effect of Public Institutions. The consideration of the effect \ 
which public institutions exert on local bills of mortality naturally j 
follows on a consideration of the eliect of migration, as the ' 
inequality arising from such institutions is due to migrations into / 
them from outlying districts. The rule in dealing with a public 



90 VITAL STATISTICS. 

iiivStitution is to deduct the deaths of those inmates derived from 
outside the district concerning whicli tlae calculation is made, at 
the same time including the deaths of inhabitants of the said 
district which may have occurred in other institutions outside the 
district. Thus, workhouses and asylums are often situated outside 
the district from Avhich they receive inmates ; and in London and 
other great towns the large public hospitals receive patients from 
outlying districts. The deaths in all these cases should be, and 
in some cases are, relegated to their respective districts.. 

The following case reproduced from the first edition of this 
book may be taken as exemplifying the methods of procedure in 
correcting a local death-rate for extra deaths occurring in external 
and internal institutions. 

The Wandsworth sub-district of the Wandsworth district 
(London, S.W.) has Avithin its borders the County Lunatic 
Asylum, the Hospital for Incurables, St. Peter's Hospital, 
Wandsworth Prison, and the Royal Patriotic Asylum for Girls; 
and it sends its sick poor to the Wandsworth and Clapham 
Workhouse Infirmary, which is outside its borders, while some 
of its inhabitants die in the large metropolitan hospitals. 

Total deaths in Wandsworth in 1885 were . . .628 
Of these there occurred in its internal institutions . 132 
In addition there occurred in the Union Infirmary and other 
outlying institutions 78 deaths. 

The mean population of Wandsworth in 1885 was 31,497. 

(1) The death-rate, uncorrected for deaths in internal institu- 
tions, and not including deaths in outlying institutions, is 

628x1000 TQOQ .-. 1 
—- = 19'83 per thousand. 

31,497 ^ 

(2) In order to ascertain the death-rate corrected for internal 
institutions without including the deaths in outlying institutions, 
we must ascertain the poiJulatioii of its institutions as well as their 
deaths. By the census of 1881 this was 1482, which may be 
taken as nearly correct for 1885. 

Corrected population = 31,497 - 1482 = 30,015. 

Corrected deaths = 628 - 132 = 496. 

T. ,, , 496x1000 ,...<. 
Death-rate = — = lb -52. 

oU,vJlD 

(3) The death-rate excluding the population and deaths of 
internal institutions, and including the deaths (but not the 



DEATH-RATES. 91 

population, because this is unknown) of Wandsworth parishioners 
in outlying institutions. 

Population = 30,015. 
Deaths- 490 + 78 = 574. 

Death-rate = ^:^'fO=19-12. 
30,015 

The last death-rate more nearly than any other represents the 
true mortality of the Wandsworth sub-district. For it excludes 
the population and deaths in its numerous internal institutions 
(to Avhicli Wandsworth contributes only an inapi)reciable cpiota), 
and it allows for the deaths of Wandsworth parishioners in ex- 
ternal institutions. The only fallacy is, that no allowance is made 
in the population for these inhabitants of Wandsworth Avho are 
in the outlying institutions without their illness proving fatal. 
This number must, however, be comparatively small, and cannot 
very materially ali'ect the result. 

Official Corrections. Each sanitary authority in London is 
supplied quarterly from the General Kcgister office with particulars 
of deaths of their inhabitants in outlying institutions, so that the 
necessary correction can be made. 

For the thirty-three great towns, the statistics published by 
the Registrar-General make corrections to the following extent : 
the deaths of non-residents are distributed to their respective 
districts in the case of the following institutions, viz., County 
Hospitals, Couniy Asylums, Infectious Diseases Hospitals, and 
Convalescent Homes. On the other hand, all deaths occurring 
in general, i.e., Borough as distinguished from County Hospitals, 
and in children's and other special hospitals, are left undistributed, 
and are included in the returns of the sub-districts in which those 
institutions are situate. 

The previous residence of persons dying in institutions is in 
each instance inserted in the death register in order to afford 
to the medical officer of health the means for obtaining the in- 
formation necessary to correct the death statistics of his district. 
It still remains true, however, that in many small urban and rural 
districts this correction is avoided, and erroneous because defective 
death-rates are published. 



CHAPTEK Xr. 

EELATIONSHIP BETWEEN BIRTH-RATE AND 
DEATH-RATE. 

INFLUENCE of Birth-rate on Age-Constitution of Population. 
The age-distribution of a poijulation, i.e., the relative number 
of persons living at different groups of ages, depends upon the 
rate and mode of increase of the population. This increase may 
be due to excess of births over deaths (natural increase) or to 
immigration. Immigration is generally of comparatively young- 
adults, and thus has an important bearing on the death-rate, 
which it tends to lower. A population such as that of England, 
with a birth-rate persistently higher than the death-rate, contains 
an undue proportion of children, of youths, and of persons of 
middle life, and so a lowering of the death-rate is produced, as in 
the case of immigration. The undue proportion of persons of 
a lower age in a po^Julation with a persistently high birth-rate 
is explained as follows : In a stationary population undisturbed 
by migration, the number of births equals the number of deaths, 
and if the rate of mortality at different ages does not vary from 
time to time and the births and deaths are uniformly distributed 
throughout each year, the age -constitution of the population 
remains uniform. The births and deaths in the stationary 
population being equal in number, the birth and death-rates 
are also identical. If now the birth-rate suddenly increases, 
the number living in the first year of life will increase ; and 
if this higher birth-rate persists, in the second year of its occur- 
rence the number living under two years of age will be increased, 
in the third year the number living under three years, and so on. 
If the high birth-rate continues for, say, 40 years, the number 
living at all ages under 40 will be increased, and so on. But for 
about twenty of these forty years a further influence will have 
been brought to bear. Those aged 20-40 who were born under 

92 



BIRTH-RATE AND DEATH-RATE. 93 

the conditions of tlio hypothesis liave children of their own ; 
so that, assuming the hirth-rate to remain stationary, the absolute 
number of births per annum is increasing rapidly every year. 
The consequence of this uninterrupted increase in the annual 
numl)er of births is, that the proportion of those living at the 
earlier ages as compared with the entire population becomes 
greater, and a distril)ution of the population is arrived at which 
we shall find is favourable to a low death-rate (page 9G). The 
diagram on page 94 should be studied in connection with the 
preceding remarks. 

The disturbing e fleet on the age of a population of a yearly 
increasing number of Inrtlis is shown in the accompanying diagram 
fi'om the supplement to the Retjistrar-GeneraTs Thirty-fifth Annual 
Report. 

The diagram represents by its area enclosed by the continuous 
dark line, the relative numT)ers of the population in eighteen 
groups of ages, as enumerated at the census of 1871. The area 
enclosed by the dotted lower line represents what the population 
would have been had the births i-emained uniformly 253,320 
a year as in 1771, instead of increasing as tliey did to 797,428 in 
1871. Thus in the population as enumerated in 1871, 3,100,000 
were living who were under the age of 5 years, while in the 
population with the stationary number of births, the numlier 
of children of that age would be one million only. It is assumed 
that no migration occurred during the 100 years. 

We have assumed in the preceding remarks that the change 
was from a stationary population to one with a birth-rate higher 
than its death-rate, but in which the birth-rate remained constant 
after it liad once increased. If, however, the birth-rate Avere con- 
tinuously to increase, the effect in disturbing the normal or Life- 
Table distrilnition of a population would be still greater, and for 
many years this Avas the state of things in England. Since 1876, 
however, the birth-rate has decreased, and, as shown Ijy the 
following figures, there was in scA-eral years an actual decrease, 
and since then only a very slight increase in the al^solute number 
of births, irrespective of population. Such a" condition of the 
factors producing population will obviously have a much less 
disturbing influence on its age-distribution than if the number of 
births Avere continuously to increase. If the total annual births 
Avere to remain stationary in number, the disturl)ance in the age- 
distribution of the ]iopulation Avould, as the Avave of population 
adA'ances, gradually disappear. 







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BIRTH-RATE AND DEATH-RATE. 



95 



Year. 


Niiniber of Births. 


Birth-Rate. 


1876 . 


887,968 


36-3 


1880 . 


881,643 


34-2 


1881 . 


88.3,642 


33-9 


1882 . 


889,014 


33-7 


1883. 


890,722 


33-3 


' 1884 . 


906,750 


33-3 


1 1885 . 


894,270 


32-5 


1 1886. 


903,866 


32-4 


! 1887 . 


886,331 


31-4 1 


i 1890. 


869,937 


30-2 


1894 . 


890,289 


29-6 


1895 . 


922,291 


30-4 


1896 . 


917,201 


29-7 


1897 . 


921,104 


29-7 



M. Bortillon gives a valuable table (p. 28, op. cit.), from Avliicli 
the f(jllo\ving particulars are derived : — 

Age Composition of the Population in European Countries 

IN 1880. 











For every 1000 inhabitants at all ages there were 


Country. 


Children. Adults. 


Old People. 


0-15 1 15-00 


CO and upwards. 


Hungary .... 373 575 


52 


Scotland 






366 556 


78 


England 






365 1 562 


73 


Germany 






354 567 


79 


Ireland 






1 351 1 553 


96 


Spain 






348 


595 


57 


Norway 






347 


563 


90 


Belgium 






335 


567 


98 


Sweden 






' 326 


581 


93 


Italy 






322 


589 


89 


France 






1 267 


610 


123 



It is evident that, with the exception of Hungary, no European 
country has so young a population, l:)ased on the average age of its 
people, as have England and Scotland. Probably this remains 
true, notwithstanding the lowered birth-rate shared by England 
and other countries in recent years. 



96 



VITAL STATISTICS. 



The following table, calculated from the English census figures 
for 1881 and 1891, shoAvs clearly the effect on the age-distribution 
of the population of the lowering of the birth-rate between the 
two census enumerations. 

Age Composition of the English Population. 



1881 . 
1891 . 


0-15 


15-CO 


00 and upwards 


Total at all Ages. 


372 
351 


563 
576 


65 
73 


1000 
1000 



Influence of Birth-rate on Death-rate. We have seen that 
the age-constitution of the population is, if migration be left out 
of account, determined by the birth-rate. The age-constitution 
of the population is of fundamental importance in relation to the 
ileath-rate, the birth-rate affecting the death-rate only in so far as 
it alters the age-constitution of the population. 

Most erroneous ideas have prevailed as to the relation between 
the birth-rate and the death-rate. The interpretation of the true 
relationship between the two depends on an appreciation of what 
has been said concerning the influence of the birth-rate on the 
age-constitution of a population. It is evident that if, owing to 
a high birth-rate, there is a larger proportion of children in one 
community than in another,- and the relative hygienic conditions 
of the two are equal, there will be more deaths of children in the 
former ; and inasmuch as the rate of mortality of young children 
is higher than that of all others except the aged, the general 
death-rate will be raised. But if the high birth-rate be contimied, 
there will not only be a . large proportion of children, but of 
others between 10 and 40 years of age, at which ages a low rate 
of mortality holds ; and this factor counterbalances the other, and 
causes a continued high birth-rate to be associated with a low 
death-rate. Speaking generally, the mortality of a population in 
which there is an excess of births over deaths should be lower 
than that of a stationary population, in which the births and 
deaths are equal in number, because in the latter case there is 
a larger proportion of old people than in the former. The only 
exception to this rule would be if emigration interfered with the 
normal effect of a high birth-rate. 

The late Dr. Letheby held, on the contrary, that "the Inrth- 
rate is the controlling element of the death-rate " ; that " an 



BIRTH-RATE AND DEATH-RATE. 97 

increase in the rate of mortality is often a sign of prosperity, for 
a high death-rate means a high birth-rate, and a higli liirth-rate is 
the invariable concomitant of prosperity." According to this 
view, a high birth-rate is a direct and mechanical cause of a high 
death-rate, owing to the great mortality among infants. This 
theory ignores the essential fact that a continuously high birth- 
rate not only causes an excess of tlie infantile population, among 
whom the mortality is great, but also an excess of persons between 
10 and 40 years of age, among whom the rate of mortality is low. 

That a high birth-rate and a high death-rate commonly co-exist 
is certain, thougli the concurrence is by no means constant, nor do 
the variations in the two follow on equal lines, as can easily be seen 
by comparing the birth and death-rates of different great towns. 

A high birth-rate usually occurs in crowded districts, there being 
in these a much higher proportion of people at child-bearing ages, 
owing to the inrush of young workers in search of the higher 
town wages. It is not surprising that in such conditions of 
life the high birth-rate should be associated with an excessive 
infantile mortality and a high general death-rate. 

So far from the high birth-rate of towns causing their higher 
death-rate when compared with rural districts, it will be hereafter 
shown (p. 108) that in nearly every great town the age-distribution 
of the population is more favourable to a low death-rate than 
that in rural districts. The higher death-rate in towns is caused 
by their less favourable conditions of life, and not by an un- 
favourable age-distribution of the population. 

Low birth-rates and low death-rates also commonly co-exist ; 
but the conclusion that one causes the other is altogether 
untenable. In France there is a low birth-rate and a high 
death-rate, owing largely to the fact that the continuous low 
birth-rate has caused the average age of the population to be 
considerably higher than in this country. Thus in 1891-95 the 
mean annual birth-rate in France was 2 2 '4 and the death-rate 
22'3 per 1000, as compared Avith a mean annual birth-rate in 
England of 30-5 and a death-rate of 18-7 per 1000. The table 
on p. 113. shows that in 1881 France, out of every 1000 persons, 
had 171 aged 55 and upwards, as compared with 105 in England. 
Under the age of 5 there were 92 in France, as compared with 
136 in England. Thus the small proportion of young children, 
which, according to Letheby, ought to have been associated with 
a low death-rate, was associated with a comparatively high death- 
rate. 



98 



VITAL STATISTICS. 



To sum up. Populations having a continuously high birth-rate 
should (sanitary conditions being equal) have loAver death-rates 
than populations having low birth-rates, because a continuously 
high birth-rate means an exceptionally large proportion of young 
adults in a population, and consequently an unduly small pro- 
portion of old people. Conversely, a low birth-rate means a 
small proportion of young adults and a large proportion of adults 
and old people, and is therefore unfavourable to a low death-rate. 

A High Birth-rate and a Low Birth-rate may both be 
followed by a Low Death-rate. Dr. E. W. D. M. Cameron 
[Public Health, vol. vii. p. 100) has constructed the following 
diagram to illustrate the direct and immediate increase of dea;th 




Fig. 6. 
Diagram illustrative of relations between birth and death-rates. 



rate produced by a high birth-rate at its first occurrence (through 
increase of infantile mortality) and the subsequent decrease of 
death-rate produced by a continued high birth-rate, through its 
influence in increasing the proportion of persons living at ages 
of low mortality. 

In the diagram the birth-rate is supposed to mount up suddenly 
and continue high for ten years, then to drop from " high " to 
"medium," go on falling gradually during the second decade, 
finally remaining uniformly low in the third decade. 



BIRTH-RATE AND DEATH-RATE. 



99 



The corresponding death-rate rises at once with the birth-rate, 
reaches its acnm n<';u' the end of the, first five years of liigh l)irtli- 
rate, and slowly declines during the second hve years. It next 
suddenly drops along with the birth-rate, continuing to fall with 
it during the next ten years. In the third decade it gradually 
rises witliout any corresponding rise of birth-rate. 

During 1881-90 a high l)irth-rate in the previous decade and 
a lower birth-rate in the current decade Avere l)oth co-operating 
to produce a low death-rate. 

A Special Illustration of Eelationship between Birth-rate 
and Death-rate. The following example illustrates the errors 
as to the relationship between the birth-rate and death-rate which 
reappear from time to time in local health reports. Dr. Yarrow, 
the medical officer of health of the parish of St. Luke, a central 
district in London, in a special report on the birth-rate and death- 
rate of the i)arish in 1887-96, endorses Dr. Drysdale's opinion 
that " if the mortality is to be lowered in St. Luke, births must 
lie reduced." If, as may be assumed, by mortality is meant the 
general death-rate at all ages, this raises the whole question of 
the relationship between the birth-rate and the death-rate, and 
the instance is worthy of detailed study. The deaths in St. 
Luke under the age of 5 exceed the total deaths at all other ages, 
which is taken by Dr. Yarrow as "proving beyond doubt that 
the infant mortality is the main cause of our heavy death-rates." 
Is this the case 1 

From what has been said in the previous paragraphs it will 
be evident that a high birth-rate, if it cause a high death-rate, 
will do so by increasing the projjortion of children under 5 who 
are subject to a higher rate of mortality than that prevailing at 
ages 5-55. 

What then is the age-distribution of St. Luke's population? 
The following table shows the number of persons out of 1000 at 
all ages which, at the census 1891, were of the following ages : — 





England and Wales. 


St. Luke. 


Kensington. 


Under 5 . 

5-55 .... 

Over 55 . 


123 
773 
104 


130 

786 
84 


89 
808 
103 




1000 


1000 


1000 



o 



100 



VITAL STATISTICS. 



It has not been thought necessary to further subdivide the 
groups of ages in the preceding comparison, but if further indica- 
tions are required they are furnished in the following table. The 
factors of correction by Avhich the death-rate of each of the above 
in 1891 must be multiplied (according to the method described on 
p. 109) are as follows : — 





England and Wales. 


St. Luke. 


Kensington. 


Factor of Correction 
Crude Death-rate . 
Corrected Death-rate 


1-0000 
21-5 
21-5 


1-08070 
30-1 
32-5 


1-10184 

18-4 

20-3 



Thus the age-distribution of St. Luke is more favourable to a 
low general death-rate than that of England as a whole, though 
not so favourable as that of Kensington. 

St. Luke and Kensington are instances of parishes which have 
had for a protracted period a high and a low death-rate respectively. 
In 1861 the birth-rate of Kensington was 30-1 ; it was 26-9 in 
1881 and 23-1 in 1891. The birth-rate in St. Luke, according 
to the Eegistrar-General's figures, was 43-3 in 1861, 45*5 in 
1881, and 42-9 in 1891. The figures for St. Luke require 
some correction, as this parish has within it a large lying-m 
Institution, receiving patients from other districts. When this 
correction Avas made for 1897 the birth-rate of 46-7 became 36-3. 
This correction does not, however, affect the fact that St. Luke 
has had for many years a relatively high birth-rate. The difference 
between the low death-rate of Kensington and the high death-rate 
of St. Luke camiot therefore be caused by any recent or sudden 
alteration in their respective birth-rates, causing in one a sudden 
increase of infants, subject as they are to a high death-rate. 

Will the steadily higher proportion of children under five in 
St. Luke's account for its general death-rate being higher than 
that of Kensington^ We will assume, to simplify the argument, 
that over the age of five the proportion of persons living at each 
age is identical in both Kensington and St. Luke. This assumption, 
as can be seen from the first of the preceding tables, favours St. 
Luke, because, although at the ages of low death-rate 5-55, it has 
a slightly smaller proportion of persons than Kensington ; at the 
ages of high death-rate, 55 and upwards, it has a much smaller 
proportion of persons than Kensington. The last factor would 



BIRTH-RATE AND DEATH-RATE. 



101 



tend to counterbalance any advantage that Kensington might 
secure by an excess of females in its population. 

On the basis of the above assumption let the death-rates of 
Kensington in 1891, at ages under five and over five, be applied to 
the population of St. Luke in 1891. 





Population of 
St. Luke, ISyl. 


Death-rate of Kensington, 

1891, per 1000 living at 

each age-group. 


Calculated No. 

of Deaths in 

St. Luke. 


Under 5 . 
Over 5 . 

All ages . 


5,529 
36,911 


64-8 
13-9 


359 
513 


42,440 


18-4 


872 



Therefore the calculated death-rate in St. Luke would be 

872 X 1000 on r 
iiO'b. 



42,440 

But the actual death-rate at all ages was 30*1, the death-rate at 
ages under five being 97"1, and at ages over five 20'1 per 1000 
living at each of these age-groups. 

And the general death-rate of Kensington in 1891 was 18*4. 
It is plain, therefore, that the ditference between 20"6 and 18'4 is 
caused by differences in age-distribution of the populations of 
St. Luke and Kensington ; but that the further difference between 
20'6 and 30'1 is caused by differences of social and sanitary 
conditions, altogether apart from any consideration as to the 
birth-rate or the age-distril:)ution of the populations. 



CHAPTEE XII. 

DEATH-EATES COERECTED FOE AGE AND 
SEX-DISTEIBUTION. 

Influence of Age and Sex-distribution on Death-rate. We 

shall consider in this chapter the means of measuring the 
modifications in the general death-rate which may result from 
varying age and sex-constitution of a population, reserving to 
the next chapter the consideration of death-rates at different 
ages. 

Dr. Ogle has summed up the influence of age and sex-distribu- 
tion of the population on death-rates in the following words : 
"It is necessary to point out that two places might be on a 
perfect equality with each other as regards their climate, their 
sanitary arrangements, their closeness of aggregation, as also 
the habits and occupations of their inhabitants, and yet might 
have very different general death-rates, owing to differences in 
the age and sex-distribution of their respective populations. 
Such a supposed case is, of course, scarcely likely to j^resent 
itself, for when the prevalent occupations are the same in two 
places the age and sex-distribution is almost certain to be the 
same also. But in places where the prevalent occuj^ations are 
not the same there are often very great differences in the age 
and sex-distribution of the populations, and such as seriously 
affect the general death-rates." 

The age and sex-distribution in a given district varies but 
slowly, thus little difficulty arises in comparing the death-rate 
of the same district or town at different periods. It is ivhen 
different districts or toAvns are compared that the necessity for 
correction for age and sex-distribution becomes imjDerative. 



102 



CORRECTED DEATH-RATES. 



103 



Mean Annual Rate of IMortality per 1000 of each Sex. 





Males. 


Females. 


1841-50. 


1801-05. 


18-11-50. 


1801-05. 


All arfes . 


23-1 


198 


21-6 


17-7 


UihIlt i) years . 


71-2 


62-1 


61.1 


520 


5-. 


9-2 


4-5 


8-9 


4-5 


10- . 


5-1 


2-5 


5-4 


2-7 


15-. 


7-1 


4-0 


7-9 


4-0 


20- . 


9-5 


5-3 


9-1 


4-9 


25- . 


9-9 


7-2 


10-6 


6-7 


35- . 


12-9 


12-2 


12-9 


10-3 


45- . 


18-2 


19-8 


16-1 


15-3 


55- . 


31-8 


36-3 


28-4 


29-8 


65- . 


67-5 


71-9 


60-9 


62-8 


75- . 


148-3 


149-9 


135-9 


136-1 


85 and upwards 


312-3 


290-6 


293-3 


263-8 



A study of the above tabic, giving the death-rate for each sex 
at various age-groups, shows that between tlie ages of 5 and 55, 
the death-rate per 1000 living at each group of ages is lower than 
the coml)inetl death-rate for all ages. Under 5 and over 55, the 
death-rate is higher than the combined death-rate for all ages. 
It is evident, therefore, that, as the proportion of the total 
population living at these different age-groups differs greatly in 
different communities, the relative numbers subject to the higher 
death-rates at the two extremes of age will differ to a correspond- 
ing extent, and consequently the relative total death-rate for all 
ages will vary. 

The age-distribution of populations is therefore of great im- 
portance in determining the relative value of their death-rates. 
If they are identical in two localities, then any differences in 
their death rates may be referred to influences j^eculiar to each 
place. 

The same reasoning applies for sex distribution. At nearly 
all ages the death-rate of females is lower than that of males. 
Consequently an excess of females (as in residential neighbour- 
hoods with a large number of domestic servants) must tend to 
lower the death-rate of a district, without implying a necessarily 
better sanitary condition. 



104 



VITAL STATISTICS. 
Census, 1891. 



Ages. 


Age-distribution of Population of 










Huddersfield. 


England and Wales. 


Norwich. 




Males. Females. 


Males. Females. 


Males. Females. 


Under 5 


475 502 


609 616 


606 617 


5- . 






491 532 


584 587 


569 575 


10- . 






534 541 


556 556 


521 550 


15- . 






513 581 


506 513 


463 566 


20- . 






474 572 


430 483 


378 506 


25- . 






782 920 


720 787 


684 805 


35- . 






583 656 


554 592 


514 593 


45- . 






413 485 


411 450 


372 463 


55- . 






250 317 


266 306 


272 351 


65- . 






119 166 


154 188 


177 244 


75 and upwards 




•26 48 


56 76 


64 110 




4660 5340 
10,000 


4846 5154 
10,000 


4620 5380 








10,000 



In the above table, and Figs. 7 and 8, which illustrate the 
same problem, I have compared with England as a whole the two 
instances among the thirty-three great English towns in which the 
age and sex-distribution of the population is respectively most and 
least favourable to a low death-rate. For males it will be seen 
that under 5, out of 10,000 persons at all ages in the standard or 
normal population of England and Wales, there were at the 1891 
census 609 males, in Huddersfield 475, in ISTorwich 606 ; and the 
corresponding number of female children Avas 616, 502, and 617 
respectively. Korwich therefore had, so far as its children under 
5 were concerned, a normal population, while Huddersfield had a 
population with a very small proportionate number at this age of 
high mortality. 

Over 55 years of age the proportionate number of males in 
England, Huddersfield, and ISTorwich respectively, was 476, 395, 
and 513, and of females 570, 531, and 705. Thus Huddersfield 
again had the lowest proportion at ages over 55 (ages of high 
mortality) of both males and females, while JSTorAvich at the same 
ages had a higher proportion of males, and a much higher propor- 
tion of females than England and Wales as a whole. 

The problem is to find a means of correcting the death-rate for 
such variations in age and sex-distribution of the population as are 
shown in the preceding instances. It can be effected in two ways. 



CORRECTED DEATH-RATES. 105 

(1) The method to he described on page 109 ; and 

(2) A statement of the deaths at various groups of ages, and in 
the two sexes, in proportion to the population in each of these age 
and sex-groups. 

The distribution of the population as to age and sex favours a 
low mortality — 

(1) In newly-settled communities. 

(2) In towns, and especially when they are rapidly increasing; and 

(3) In manufacturing as compared with agricultural neigli- 
bourlioods. 

The high mortality which usually holds in such populations would 
be still higher but for their favourable age and sex-constitution. 

Dr. Ransome gives an example Avliich may serve as a further 
illustration of differences in the general death-rate, due simply to 
varying age-distribution of pojjulation. Suppose two towns, A and 
B, each with 1000 inhabitants, and exactly alike in their sanitary 
conditions. A has 150 children under 5; B has only 100 under 
5, which in each case die at the rate of 10 per cent, per annum, 
Avhile persons over 5 die at the rate of 10 per mille. Reckoning 
up the total mortality per 1000 at all ages, we find that 

In A, out of 150 children, 15 die. 
„ „ 850 over 5, 8'5 die ; equal to 23'5 per 1000 of the 
entire population. 

In B, out of 100 children, 10 die. 

„ 900 over 5, 9 die ; equal to 19-0 per 1000. 

Thus there is a difference of 4"5 per 1000 in the death-rate, due 
simply to differences in the composition of the two populations, 
and apart altogether from their state of health. 

Dr. Ransome further points out that a death-rate of 10 or even 
12 per 1000, which is not infrequently recorded in certain favoured 
districts, cannot be regarded as a true measure of longevity of its 
inhabitants. A death-rate of 10 per 1000 means either that every 
child l)orn attains the age of 100 Ijefore he dies, or else that the 
average age at death is 100, and that if some die in infancy, others 
must have lived much more than 100. Similarly, a death-rate 
of 12 per 1000 means an average age at death of over 80. " Under 
present conditions such figures are not attained by any community 
in the world, and can only be looked for in the millennium, when, 
as Isaiah says, the child shall die an hundred years old." 

Method of Correction for Age and Sex-distribution. The 

Registrar-General commenced, in his Annual Summary for 1883, 



p- £. 



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108 



VITAL STATISTICS. 



the following metliod of correcting the death-rates in the great 
towns, giving in parallel columns the recorded and corrected 
death-rates for each town. This has been continued for sub- 
sequent years, and I append the table for 1897, the towns being 
arranged in the order of their corrected death-rates. 

Eecoeded and Corrected Death-rates per 1000 Persons living 
IN 33 Great Towns in 1897. 



Towns, 

ia the order of 

tlieir Corrected 

Death-rates. 


Standard 
Death-rate. 


Factor for 
Correction 
for Sex and 
Age Dis- 
tribution. 


Recorded 

Death-rate, 

1S97. 


Corrected 

Death-rate, 

1897. 


Comparative 

Mortality 

Fiinire, 

1S97. 


Cols. 
England & "Wales 


1. 


2. 


3. 


4. 


5. 


19-15 


1-0000 


17-43 


17-43 


1000 


England and 


) 










Wales, less the 


19-45 


0-9845 


16 52 


16-26 


933 


33 Towns 


J 










33 Towns 


17-71 


1-0813 


19 


10 


20-65 


1185 


Croydon . 


18-37 


1-0424 


13 


07 


13-62 


781 


Brighton . 


18-94 


1-0110 


15 


06 


15-23 


874 


Portsmouth 


18-73 


1-0224 


16 


21 


16-57 


951 


Cardiff . 


17-16 


1-1159 


14 


94 


16-67 


956 


West Ham 


17-75 


1-0788 


15 


66 


16-89 


969 


Swansea . 


17-53 


1-09-24 


15 


82 


17-28 


991 


Derby 


17-36 


1-1031 


16 


03 


17-68 


1014 


Bristol 


18-33 


1-0447 


17 


20 


17.97 


1031 


Norwich . 


19-99 


9579 


18 


77 


17-98 


1032 


Halifax . 


17-20 


1-1133 


16 


48 


18 35 


1053 


Plymouth . 


19-70 


0-9720 


19 


04 


18-51 


1062 


Huddersfield 


16-47 


1-16-27 


16 


40 


19-07 


1094 


Leicester . 


17 64 


10855 


17 


66 


19-17 


1100 


London 


17-97 


1-0656 


18 


19 


19-38 


1112 


Hull 


18-23 


1-0504 


IS 


56 


19-50 


1119 


Gateshead . 


17-83 


1 0740 


18 


28 


19-63 


1126 


Bradford . 


16-73 


1-1446 


17 


45 


19-97 


1146 


Birkenhead 


17-42 


1-0993 


IS 


26 


20-07 


1151 


Nottingham 


17-81 


1-0752 


18 


78 


20-19 


1158 


Sunderland 


18-25 


10493 


19 


70 


20-67 


1186 


Newcastle . 


1758 


10892 


19 


09 


20-79 


1193 


Blackburn 


17-05 


1-1231 


19 


50 


21-90 


1256 


Oldliam . 


16-72 


1-1453 


19 


18 


21-97 


1260 


Leeds 


17-28 


1-1082 


19 


88 


22-03 


1264 


Burnley . 


16-67 


1-1487 


19 


51 


22-41 


1286 


Wolverhampton 


18-30 


1-0464 


22 


05 


23-07 


1324 


Sheffield . 


17-22 


1-1120 


21 


20 


23-57 


13.52 


Birmingham 


17-33 


1-1050 


21 


59 


23-86 


1369 


Bolton 


16-90 


1-1331 


21 


97 


24-89 


1428 


Manchester 


16-90 


1-1331 


23 


10 


26-17 


1501 


Liverpool . 


17-44 


1-0980 


24 


37 


26-76 


1535 


Preston 


17-42 


1-0993 


24 


36 


26-78 


1536 


Salford . 


17-03 


1-1244 


23-91 


26-88 


1542 



CORRECTED DEATH-RATES. 109 

In the preceding table the Standard Death-rate signifies the 
deatli-rate at all agos, calculated on tlie hypothesis that the rates 
at each of twelve age-periods in each town were the same as 
in England and Wales during the ten years 1881-90, the deatli- 
rate at all ages in England and Wales during that period having 
been 19-15 per 1000. 

The Factor for Correction is the figure by which the recorded 
Death-rate should be multiplied in order to correct for variations 
of sex and age-distribution. 

Tlie Corrected Death-rate is the recorded death-rate multiplied 
by the Factor for Correction. 

The Comparative Mortality Figure represents the Corrected 
Death-rate in each town, compared with the Recorded Death-rate 
at all ages in England and Wales in 1897 taken as 1000. 

The figures in this column may be read as follows : After 
making approximate correction for differences of age and sex- 
distribution, the same number of living persons that gave 1000 
deaths in England and Wales in 1897 gave 781 in Croydon, 874- 
in Brighton, etc., etc., and 1542 in Salford. 

The first column in tlie preceding talkie is obtained by assuming 
that the mean mortality in England and Wales in 1881-90 held 
good in each town. The age and sex-distribution of each town 
at the last census being known, the mean mortality in England 
and Wales, 1881-90, is applied to the population thus constituted, 
and we have as a result the series of death-rates in column 1. 
The diff"erences between the various towns in this column are 
consequently caused simply and solely by diff'erence in age and 
sex-distribution. As an example of the method of obtaining 
these sfaiidard- death-rates Huddersfield may be taken (see table 
on following page). 

Here the total population of Huddersfield in 1891 =95,420 

The total number of calculated deaths = 1,572 

The standard death-rate is therefore 



1572x1000 T^ ,« 1^^^ 
-^^4^0" = 1^-^^P^^-1^^^' 



95,420 

which corresponds Avith the rate given in the table on p. 108. 

Now the annual death-rate of England and AVales in 1881-90 
was 19'15. This ought to be the same as the calculated death- 
rate for Huddersfield, which has been obtained by applying the 
mean annual death-rate of England and Wales at the different 
age-groups to the population of Huddersfield at these age-groups. 



110 



VITAL STATISTICS. 





Mean Annual Death- 








rate in England and 


Population of 


Calculated number 


Ages. 


Wales lSSl-90 per 


Huddersfleld 


of Deaths in 




1000 living at each 


in 1891. 


Huddersfleld. t 




group of ages.* 








Males. Females. 


Males. Females. 


Males. Females. 


Under 5 


61-59 51 


95 


4551 4785 


280 249 


5- . 






5-35 5 


27 


4691 5081 


25 27 


10- 








2-96 3 


11 


5113 5165 


15 16 


15- 








4-33 4 


42 


4905 5549 


21 25 


20- 








5-73 5 


54 


4541 5461 


26 30 


25- 








7-78 7 


41 


7466 8834 


58 65 


35- 








12-41 10 


61 


5576 6265 


69 66 


45- 








19-36 15 


09 


3944 4649 


76 70 


55- 








34-69 28 


45 


2393 3017 


83 86 


65- 








70-39 60 


36 


1128 1590 


79 96 


75 and upwards 




162-62 147-98 


250 466 


41 69 

773 799 

1572 






44,558 50,862 


Tot 


als 








• 


95,420 



* The death-rates for England and Wales are the means of the annual death-rates 
in 1881-90 {Registrar-General's Fifty-fourth Annual Report, Tables 11 and 12.) 
t The " calculated deaths" are taken to whole numbers only. 

But the death-rate for Huddersfleld is loioer, as shown above, 
which must arise from the fact that the distribution of age and 
sex in the Huddersfleld population is more favourable than in the 
country generally. That this is so can be seen from the table on 
p. 104 and by a glance at figures 7 and 8. 

The standard death-rate being lower for Huddersfleld must be 
raised in a certain ratio in order to bring it into comparison with the 
death-rate of England and Wales — i.e., it must be increased in the 

19-15 

proportion of 16-47 to 19*15. "^ ■ ■' 



But the fraction 



= 1-1627. 



16-47 

This, then, is the factor for correction for age and sex-distribu- 
tion by which the recorded death-rate of Huddersfleld must be 
multiplied in order that it may be comparable with that of 
England and Wales. It may be objected that the mean age 
and sex-distribution of the decennium 1881-90 is assumed in the 
above calculation to hold good for every year of the succeeding 
decennium. This, however, can be proved to be approximately 
accurate, inasmuch as in populations whose chief occupations 
remain the same the age and sex-distribution do not alter greatly 
in a single decennium. It may be objected again that the factor 



CORRECTED DEATH-RATES. Ill 

or correction figure, ^vllicll is accurate wlien applied to the rate 
of an entire decade, may not be equally accurate for each year 
of that decade. But on selecting for comparison two years, one 
extremely hot and therefore dangerous to the young, and the other 
extremely cold and dangerous to the aged, the Registrar-General 
found that the error due to the use of the decennial correction 
figure as a constant, instead of a sjiecial correction figure for 
each year, was so small that it might practically be disregarded. 

By multiplying the recorded death-rates in column 3 (p. 108) 
l)y the factors for correction, we obtain the corrected death-rates 
given in column 4. These are the death-rates which would have 
been recorded in each town had its population been identical, so 
far as age and sex-distribution are concerned, with the population 
of England and Wales. 

Tmstwortliiness of General Death-rates. The following 
remarks of the Registrar-General (Annual Summary, 1883) on 
this point are apposite : " It may naturally be asked, of what 
use are the general death-rates, as usually given, if they cannot 
be accepted without further and considerable correction? In 
the first place, if the death-rate in any given town or other 
area in one year be compared with its death-rates in other 
years, no correction is required ; for the age and sex-distribu- 
tion in an individual town or other area remains practically 
constant ; and, secondly, although it is doubtlessly true that the 
general death-rates of towns or other areas cannot safely be used 
for accurate comparison between such toAvns or areas in respect of 
healthiness without further correction, yet they serve as a very 
valuable approximate indication ; for if the column 3 be com- 
pared with column 4, it will be seen that whether the towns 
be arranged according to their recorded or according to their 
corrected death-rates, the order will scarcely be changed. The 
correction simply alters the amount of difference between the 
towns, leaving the position in which they stand to each other but 
slightly changed." 

Instances of Necessity for Correction. In the table on p. 108 
it will be seen that only in two of the thirty-three towns, 
Plymouth and K"orwich, is the corrected death-rate lower than 
the recorded death-rate. In all the other towns a correctional 
addition to the recorded death-rate is required, varying in amount 
from 0-17 to 3-07. 



112 



VITAL STATISTICS. 



This fits in with the general rule that in rural districts the age 
and sex-distribution of the population is less favourable to a low 
crude death-rate than that in urban districts. In the adminis- 
trative county of West Sussex the factor of correction, calculated 
by Dr. Kelly, is -92205, and the crude death-rate of 13-27 in 1897 
becomes 12-24. In 1871-80 the mean annual death-rate in 
London and Lancashire, taken by Dr. Ogle to represent the urban 
population, was 23-69 per 1000, while the rate in twelve rural 
counties Avas 19-14. But had the rural population had the same 
age and sex-distribution as Avas the case in the urban population, 
its general death-rate would have been only 16-33. Thus the true 
comparison between urban and rural death-rates should have been 
between 23-69 and 16-33, and not between 23-69 and 19-14. 
{Bulletin de VInstitut International de Statistique, tome vi. p. 83.) 

In health-resorts the amount of correction required is usually 
greater than in the great towns, the constitution of the population 
being extremely abnormal. Brighton, one of the great towns, is 
an exception to this rule, and Worthing and Littlehampton, the 
factors of correction of which have been calculated by Dr. Kelly, are 
even more remarkable exceptions. With the exceptions mentioned, 
the following factors of correction have been calculated by me : — ^ 









Population 

estiiaated in 

the middle of 

1S97. 


Factor of 
Correction. 


Death-rate, 1897. 




Crude. 


Corrected. 


Brighton . 

Hove 

Eastbourne 

Margate . 

Bournemouth 

Worthing . 

Littlelianipton 






121,401 
34,331 
46,698 

58,820 

20,100 

5,800 


1-0110 
1-0542 
1-1248 
1-1363 
1-1368 
-99300 
-99871 


15-1 
13-7 

8-2 

10-1 
13-5 
12-2 


15-3 

14-4 

9-2 

11-5 
13-4 
12-2 



Dr. Tatham {Supplement to Fifty-fiftli Anmial Report Registrar- 
General, part i. p. xxxviii.) instances ten urban districts, in all of 
which the crude death-rate was about 19-8 per 1000, but in which 
the rates, when adjusted for differences of age and sex-constitu- 
tion of population, were found to range between such extremes as 
16-6 per 1000 (Bridge), and 21-9 (Dewsbury). In the same volume 
are given the crude and corrected death-rates for males and females 
in every registration county of England and Wales. In comment- 
ing on this subject, Dr. Tatham remarks : " It is futile to compare 



CORRECTEl) DEATH-RATES. 



113 



the crude death-rates of different districts unless their populations 
are known to be alike with respect to age and sex-constitution." 

From an international standpoint, corrected death-rates arc also 
of great importance, and it is unfortunate that but scanty data are 
available. The following instance of the extent of correction 
required is given by Dr. Ogle. In 1881 the general death-rate in 
England and Wales was 18*9 per 1000 of all ages, while the general 
death-rate in France was 22'0, i.e., 3'1 higher than England. But 
had the age distribution of the French population lieen identical 
with that of the English population, the French general death-rate 
Avould have been 20-9, and not 22-0. Thus of the 3-1 difference 
between the two rates, 2*0 was due to difference of health con- 
dition, and 1"1 was due to differences of age-distribution. 

Dr. Ogle, at the meeting of the International Institute of 
Statistics in Vienna, 1891, proposed the establishment and inter- 
national use of a Standard Population, with fixed age and sex- 
distribution in the calculation and comparison of marriage, birth, 
and death-rates. He gives in his paper a comparative table of 
the age and sex-distribution of the population in England and 
Wales (1881), Austria (1880), Switzerland (1880), Germany 
(1880), Holland (1879), France (1881), and Italy (1881), from 
which the following particulars are taken : — 



Ages. 


Age and Sex-distribution of Population per 


lO.COO. 


England and 
Wales (1880). 


Germany 
(1880). 


Frar.ee 
(1881). 


Aggregate of 

the above 

seven European 

Countries. 




Males. Females. 


Males. Females. 


Ma'es. FenialeF. 


Males. Females. 


0- 5 . 


677 679 


685 681 


466 458 


617 611 


5-10 . 


604 608 


572 573 


4.59 451 


541 537 


10-15 . 


540 539 


519 516 


425 415 


491 485 


15-20 . 


488 492 


465 471 


436 431 


460 466 


20-25 . 


428 468 


421 437 


437 468 


427 447 


25-35 . 


701 759 


691 726 


698 681 


700 725 


35-45 . 


546 587 


577 609 


665 6.54 


606 625 


4.5-55 . 


398 439 


430 465 


566 577 


472 499 


1 5.5-65 . 


278 312 


326 365 


447 457 


358 381 


fi.5-75 . 


150 178 


166 190 


276 '>90 


194 'J09 


75-85 . 


50 64 


49 57 


100 112 


63 70 


85 & upwards 


6 9 
4866 51.32 


4 5 
4905 5095 


13 18 
4988 5012 


7 9 
4936 5064 


All ages 




10,000 


10,000 


10,000 


10,000 



114 VITAL STATISTICS. 

Applying the death-rates at each age-period in England and 
Wales in 1881 to the several populations, and adding np in each 
case the numbers of deaths among males and females at each 
age-period, Dr. Ogle found that with identical death-rates at each 
age and in each sex, the general death-rate — that is, the death-rate 
as usually calculated — would be : — 

18-88 per 1000 in England and Wales. 

18-82 „ „ Austria. 

19-38 ,, ,, Switzerland. 

19 '21 „ ,, Germany. 

20-18 „ „ Holland. 

21-31 ,, ,, France. 

19-33 „ „ Italy. 

Dr. Ogle remarks, "Were these death-rates put before the 
general public, they would scarcely escape falling into serious 
error, for they would almost certainly ascribe to difference of 
healthiness differences merely due to the different composition of 
the populations in regard to age and sex." To avoid this. Dr. Ogle 
proposed that the population in the preceding table representing 
the aggregate population of seven European states (about 170 
million persons) should be taken as a standard for general inter- 
national use. 

Dr. Korosi of Budapesth adopts Sweden as his standard popu- 
lation, and employs a distribution of ages only,* dividing the 
population into four periods only, viz. : — 



All under one year. ' 
One to twenty years. 



Twenty to fifty years. 
All over fifty years. 



This does not apjDear to admit of such exact correction for age- 
distribution as the population proposed by Dr. Ogle, and makes no 
correction for sex-distribution. The classification of ages is un-' 
satisfactory, ip. view of the tendency for the ages of persons both 
at the census and in the death-returns to be entered in round 
numbers at each decennial period (see figure 1, page 3) ; and it is 
doubtful if the subdivision of ages is sufficient to ensure accuracy. 

The subject of correction for age and sex-constitution of popula- 
tion will require further consideration in connection with special 
causes of mortality (pp. 188 and 215), and with the fatality from 
various diseases (p. 338). 

* Mortalitiits Coefficient ii. Mortalitats Index, Berechnnng des Internat. 
Sterblichkeits Indexes fiir 14 Staaten, J. Korosi, Int. Statist. Bulletin 6, 
1892, p. 305. 



CHAPTER XIII. 
MALE AND FEMALE MORTALITY AT DIFFERENT AGES. 

IN" the last chapter, the disturbing influence of varying age and 
sex-distribution of the population on the general rate of 
mortality has been discussed, and the method by which the fallacy 
involved can be avoided has been described. 

Death-rate at Age-periods. — A statement of the deatli-rate at 
various groups of ages per 1000 living at these ages, is also quite 
trustworthy for comparison with other towns and districts. To 
obtain this, it is necessary to know — 

1. The population at dillerent age-groups. 

2. The deaths at different age-groups. 

The latter are obtained from the local registrar's death-returns ; 
the former may be ascertained in the case of each urban and rural 
sanitary authority by an application to each group of ages of the 
same method of estimation for increase of population as that 
described on page 6. It is assumed that the rate of increase of 
population in each age-group is the same as holds good for the 
total population at all ages. Thus, if the numbers living at each 
age-group in 1881 and 1891 are known from the census returns, 
the calculation is short. If the age-constitution of the population 
in question at the 1881 census is unknown, the following method 
will give an approximately accurate result. It is assumed that the 
age-distribution does not vary between the two census enumerations, 
an assumption approximately correct when the prevailing industry 
in a given neighbourhood has not altered. Then the total jjopula- 
tion in 1881 and in 1891, and the population distributed according 
to age and sex in 1891 being given, the finding of the distributed 
population of 1896 is a mere question of proportion. 

Thus, if the total population of a town in 1891 is 107,546, 
and the number living aged 10-15 is 10,741, while the total 
population in 1881 is 92,481, to find the number living aged 
10-15 in 1896, the calculation Avill be in three stages. 

115 



116 VITAL STATISTICS. 

(1) Find the rate of increase per unit of population from 1881 
to 1891. 

92,481(1 +r)io = 107,546. 
Therefore log. (1 + r) = ^iy (log. 107,546 - log. 92,481). 
Therefore l+r= 1-015. 

Where r = rate of increase per unit of population = '015. 

(2) Find from this the total mean population for 1896, i.e., 
after a lapse of 5-^- years. If P = mean population of 1896. 

P= 107,546 (l-015p'- 
Hence P= 116,363. 

(3) Find in this population the number living aged 10-15. 

li x = this number, 

Then 107,546 : 116,363 : : 10,741 lic. 

Therefore a; =11,625. 

There are two false methods of estimating the rate of mortality 
at different ages. The first of these is to calculate the proportion 
of deaths to total deaths • and the second to calculate the 
proportion of deaths at various age-groups to the population at 
all ages. The fallacy involved in the first method arises from 
the fact that either a diminution in the total deaths or an increase 
in the deaths at any age-group Avould increase the proportional 
deaths at the age group under consideration, though its interpreta- 
tion in the two cases would be essentially different. Or if a 
reduction in both the total deaths and the deaths at a given age- 
group occurred, this reduction might be entirely hidden by the 
statement of the result as a proportion between the two. 

The second method is equally fallacious ; as apart from any con- 
ditions adverse to health, the number of deaths at various age-groups, 
and therefore the proportion of these to the entire population, will 
vary with the number living at the same age-groups. 

For small "poindations a too minute* division of age-groups 
is unadvisable. Deductions from a small number of individual 
facts are seldom so trustworthy as when the basis on Avhich an 
inference is founded is wider, and accidental causes of variation 
are thus to a large extent eliminated. 

The tables on pp. 103 and 110 give the death-rates at various 
age-groups per 1000 living at these age-groups at various periods. 

It will be seen that under 5 and over 55 the death-rate per 
1000 living at each group of ages is higher than the general 
death-rate at all ages ; while at ages between 5 and 45 the 
mortality in both sexes is lower than the general death-rate, being 



MALE AND FEMALE MORTALITY. 117 

at its lowest ebb between 10 and 15, and much lower between 
5 and 25 than at succeeding ages. It is evident, therefore, that 
the age-distribution Avliich would be most favourable to a low 
mortality is one containing an undue proportion of persons aged 
5 to 25 — such a population as would naturally arise from a 
continuously high birth-rate. Between 45 and 55 there is a 
difference between the two sexes. In 1891-95 among men aged 
45-55 the death-rate was 19*8, identical witli that for all ages; 
among women aged 45-55 the death-rate was 15 "3, or 2 '4 per 
1000 below that for females of all ages. 

Infantile Mortality will be separately discussed in the next 
chapter. 

Death-rates at other Age-periods. The tables on pp. 103 and 

110 and figures 8 and 11 should be studied, and the remarks on 
the death-rate at different ages on p. 103. The death-rate of 
children under 5 years of age, which, like all other rates, should 
be calculated on the number of persons living at these ages, forms, 
probably, a more important hygienic test than the death-rate at 
any subsequent age-period. The changes which have occurred 
between 1846 and 1896 in the death-rate at different age-groups 
in the two sexes may be studied in Tables 13 and 14 of the 
Re(jistrar-GeneraVs Annual Report. 

Dr. Farr adopted a quinquennial grouping of ages before 25, 
and after this age a decennial, odd figures being selected as the 
limiting ages of the groups (25-35, etc.). This method was 
adopted in order to avoid the fallacy caused by the tendency 
which both the census and death-returns show to state ages at 
round figures as 20, 30, etc. It might be supposed that smaller 
groups of years would give more valuable results ; but in view of 
the preceding consideration, the elaboration of groups would 
evidently tend to diminish the true value of the results obtained. 
Dr. Farr states the case against further differentiation of groups 
thus : " In exhibiting such an abstract, I should commit a fault 
Avhich I deem it most important to avoid — that of assuming the 
delusive appearance of more minute accuracy than actually exists." 

Effect of Sex on Mortality. The table on p. 103 shows that 
female mortality Avas loAver than male mortality at all ages except 
5-20 in the years 1891-95. 

At the ages 5-10 and 15-20 the tAvo sexes had an equal death-rate. 
Between 10 and 15 female Avas slightly higher than male mortality. 

The dangers connected Avith child-bearing do not prevent the 



118 



VITAL STATISTICS. 



general female mortality at child-bearing ages from being lower 
than that of males. 

From Avhat has been stated, it will be evident that an excess of 
females, at any ages except 5-20, Avould tend, though but slightly, 
to lower the general rate of mortality. Eesidential toAvns and 
watering-places appear slightly healthier than they are, owing, 
among other reasons, to the large proportion of domestic servants 
at ages Avhen they are least prone to illness and death. The 
female death-rate is generally lowest in the towns in which the 
excess of the female population is greatest. 

The comparative crude death-rates of males and females for 
successive groups of years are shoAvn in the following table : — - 

Death-rate at all Ages op Males and Females 
(England and Wales). 



Years. 


Males. 


Females. 


1838-40 . 


23-3 


21-5 


1841-50 . 


23-1 


21-6 


1851-60 . 


23-1 


21-4 


1861-70 . 


23-7 


21-4 


1871-80 . 


22-7 


20-1 


1881-90 . 


20-3 


18-1 


1891-95 . 


19-8 


17-7 


1896 


18-1 


16-1 



Thus between 1841-50 and 1891-95, the death-rate of males 
has declined to the extent of 14-3 per cent., and of females, 18-1 
per cent. We have already seen that the proportion of boys to 
girls at birth in the English population is steadily declining 
(p. 81), and that even in the first year of life the prospects of 
life in the female are superior to those in the male. 

It might be inferred that inasmuch as (a) the proportionate 
number of males with their higher rate of mortality is diminish- 
ing in the population, and (h) the female death-rate is decreasing 
at most ages more rapidly than the male, the recent improvement 
in general mortality is due to these causes, and not to an improve- 
ment of the condition under which the male population lives. 
As shoAvn in the above table, the difference betAveen the male and 
female death-rates in 1891-95 was 2-1. The disturbing influence 
of sex-distribution on the general death-rate might therefore con- 
ceivably be considerable. If Ave imagined the entire population to 
consist of females, Avithout any alteration in conditions of life, the 



MALE AND FEMALE MORTALITY. 



119 



= 1000 



55 and upwards 

... 47 

... 57 

... 97 = 1000 

... 111 = 1000 



cleatli-ratc would become 17-7 instead of 19-8. The excess of 
female population actually present in any district has, however, 
only a com[)arative]y small iulhience on tlie general death-rate, and 
such errors as exist can easily 1)e rectified by the method of correc- 
tion for age and Hex-distril)ution already descriljcd (p. 109). 

Population at Census 1891. 

Under 5. 5-55. 

Number at eacli age out of 1000 ) Male 61 ... 376 

at all ages iu both sexes. / Female 62 ... 397 

Number at each age out of 1000 ) Male 126 ... 777 

of each sex. ) Female 120 ... 769 

The preceding table shows tlie variation in age composition of 
the two sexes. Among females tliere is a much larger proi)ortion 
of very aged persons and a smaller proportion of young children 
than among males. For this reason, in a strictly accurate com- 
parison between the sexes, it is necessary to calculate, by means of 
tlie rates at the successive age-periods, the mortality in a standard 
million of poi)ulation. The standard million adopted {Supploneut 
to Fift II -fifth Report of the Regisirar-Geneval, part i. p. xxxvii.) is a 
million having tlie age-distribution of the entire country in 1881- 
90. The mean population in 1881-90 is reduced to an average 
million of persons constituted as follows : — 



Age. 


Males. Females. 


0- . . . 


64,122 64,557 


5- . . . 


59,333 59,673 


10- ... 


54,806 54,765 


15- ... 


49,720 50,287 


20- ... 


42,922 47,564 


25- ... 


71,131 77,499 


35- ... 


55,095 58,944 


45- ... 


40,472 44,478 


55- ... 


27,151 30,893 


65- 


15,184 18,326 


75 and upwanLs 


5,591 7,487 


All ages . 


485,527 514,473 




1,000,000 



The causes of the higher mortality amoivj men are largely 
connected with the greater hardships and dangers of their occu- 
pations. These will be fully discussed in Chapter XVII. The 
greater amount of intemperance among men has no inconsiderable 
influence in the same direction. 



CHAPTER XIV. 
INFANTILE MORTALITY 

IISTFANTILE POPULATIOK". In considering the mortality 
at different ages, the first group of ages (under 5) requires 
further consideration, and especially the mortality under one year 
of age (infantile mortality). In order to ascertain the infantile 
mortality, it is necessary to know the infantile population. And 
in this case the census enumerations do not give us trustworthy 
information. The ages of infants are very commonly incorrectly 
returned at the census. The number under one year old is 
certainly understated (man}" in their first year being returned as 
one year old). A smaller number in. their second year are 
returned as two years old, and so on. It has been sought to 
explain the deficiency of infants returned at the census by 
omissions in enumeration, but Dr. Farr has attributed it rightly 
to confusion between the current year of age and the completed 
years of life, rather than to actual omissions. On account of 
this deficiency in the census number of infants, it is preferable 
to estimate their mortality in })roportion to every thousand births. 
A more strictly correct plan would be to take the mean of the 
births of the current and the immediately preceding year as 
giving the true infantile population ; but as this plan is not 
usually adopted, for the sake of uniformity the births of the 
current ye;vr are taken. 

Infantile Mortality. The infantile mortality then is the 
annual number of deaths of infants under one year of age to 
e\'ery thousand births during the same year. The rate of 
infantile mortality is regarded as a most reliable test of the 
sanitary condition of a district, owing to the fact that migration 
does not greatly affect the result at this early age. If the 
"sanitary condition" be regarded as including the complex con- 
ditions comprised in differences of social status, this is doubt- 
loss correct. Dr. Rumse}^ held that premature births should be 

120 



INFANTILE MORTALITY. 121 

.struck out of account l>otli of tlie living and dying. It sliould 
he remembered tliat still-births are in this country excluded from 
legistration, though in France they are included. The best plan 
wouM be to insist on registration in every case, making a class 
se))arate from births and deaths, in which still-births and pos- 
siljly premature births would find a logical jjlace. 

The infantile mortality in 189f3 in Enghind and Wales was 147"5 
per 1000, and corresponded almost exactly with the mean rate 
in the preceding ten years. In registration counties the infantile 
mortality in the ten years, 1885-94, ranged from 98 in Dorset- 
shire, 104 in Wiltshire and Westmoreland, and 109 in Berkshire, 
to 153 in London, 157 in Durham, 161 in Staffordshire, and 170 
in Lancashire. Among the great towns in 1897 it ranged from 
131 in Iluddersfield, and 135 in Croydon, to 220 in Burnley, 
and 2G2 in Preston. In London it was 159, as comjjared with 
an average of 155 in the ten preceding years. That the differ- 
ences in infantile mortality are not casual is shown by their %/ 
repetition year after year, the general rule being that the rate 
is highest in mining districts and those with textile industries, 
and lowest in purely agricultural districts. 

Mortality of Infants in each Month of First Year. Life 

is most liable to jjerish in its earliest stages, " the liability de- 
creasing in something like geometrical progression until the body 
becomes developed and the reproductive function is established, 
when the chances of destruction again increase, the succession 
of the species being thus secured" (Rumsey). With each week / 
after birth the danger of death diminishes. For this reason 
it is advisable in dealing with large populations to state the 
monthly or even weekly mortality of infants. The rate of mor- 
tality of boys in every month of the first year of life exceeds 
that of girls, so that, in spite of the much larger number of boys 
at birth, they are fewer in number than girls at the end of the 
first year. 

In the Fifty-fourth An7iual RepoH of the Rerjistrar-General 
(1891) is a very important discussion of infantile mortality. 
This embodies the experience of infantile mortality in three 
selected towns — Preston, Leicester, and Blackburn — Avhich almost 
invariably occupy the highest i)Osition in infantile mortality, of 
five mining or industrial counties — Staffordshire, Leicestershire 
Lancashire, W. Riding, and Durham, — and of three agricultural 
counties — Hertfordshire, Wiltshire, and Dorsetshire. 



122 



VITAL STATISTICS. 



Infantile Mortality, 1889-91. 



Age. 


Of 1000 born, the Numbers 
surviving at each Age. 


Annual Death-rates per 1000 

living in each successive 

interval of Age. 




Five 






Five 






Three 


Minins; and 


Three 


Three 


Mining and 


Three 




Rural 


Manufac- 


Selected 


Rural 


Manufac- 


Selected 




Counties. 


turing 
Counties. 


Tovi'ns. 


Counties. 


turing 
Counties. 


Towns. 


At Birth . 


1000 


1000 


1000 


213 


331 


382 


3 Months 


948 


921 


909 


75 


154 


240 


6 „ 


931 


886 


856 


61 


128 


180 


12 „ 


903 


831 


782 


— 


— 


— 



The differences in the death-rates and survivals at each period 
of three or six months speak for themselves. 

The same report contains an infantile life-table for the preceding 
three rural counties and three towns (p. xii). From this it can be 
gathered that the mortality is highest in the first day of life, and 
then falls rapidly, though still high in the remaining days of the 
first week. The mortality falls enormously in the second week, 
remains at nearly the same level through the third, and shoAvs a 
considerable decline in the fourth week. In the second month the 
mortality is only a small fraction of that in the first month; it 
then falls more gradually to the end of the seventh or eighth month, 
after which but little change occurs. Comparing the town rate 
with the rural rate, in the whole year 218 deaths occur in the 
former, and only 97 in the former out of 1000 births. This higher 
death-rate holds good throughout the entire year. Furthermore, 
it is in the later months that the chief excess of mortality occurs 
in the urban rates. Thus, in the first week of life the toAvn rate 
exceeds the rural rate by 23 per cent., in the second Aveek by 
64 per cent., in the third Aveek by 83 per cent., and in the fourth 
week by 97 per cent. Similarly in the first month the toAvn rate 
is 27 per cent, above the rural rate, in the second month 121 per 
cent, above it; the excess going on increasing until in the sixth 
month it amounts to 273 per cent., its highest point, though the 
excess does not decline to a much loAver point throughout the 
rest of the year. 

Healthy District Experience of Infantile Mortality. Since 
the Fifty-fourth Annual liejjort of tJie Registrar-General appeared. 



INFANTILE MORTALITY. 



123 



ilie chief contents of wliicli relating to infantile mortality have 
heen summarized in the preceding paragraph, the New Healthy 
District Life-tahle, by Dr. Tatham, has been published {Sup^ilevient 
Fiffij-fiffli Report of the Reriistrar-General, part ii. p. cii.). This is 
based on the experience of one-sixth of the Avliole population of 
England and Wales (4,606,503 persons), Avhich had death-rates in 
a standard population below 15 per 1000 in 1881-90. 

The death-rate among infants under one year, as shown by this 
life-table, is even under the most favourable circumstances very 
liigh ; an equally high death-rate not being again experienced until 
the age of about 80 years. About half of the first year's mortality 
occurs in the first three months. 

Experience of 1881-90. 
Number of Survivors at each age out of 1000 live-born. 





Males. 


England and 
Wales. 


Mancliester 
Township, 


Selected Healthy 
Districts. 


Born .... 

3 months 

6 do. 
12 do. ... 

Born .... 

3 months 

6 do. 
12 do. 


1000 
921 

889 
839 


1000 

895 
846 
769 


1000 
936 
914 

881 


Females. 


1000 
938 
911 
869 


1000 
918 
975 
808 


1000 
951 
934 
907 



It is evident that the gain from being born in a healthy district 
is even greater in the latter nine than in the first three months of 
the first year of life, thus strongly confirming the figures given in ^ 
the preceding paragraph from three selected counties and towns. 

Causes of Death among Infants. In the following table the 
deaths of male and female infants under one year of age in 
England in the year 1895, are arranged in the order of the number 
of deaths from each cause. It will be observed that the deaths 
are also stated for each sex in proportion to the infantile popula- 
tion ; i.e., the nearest approximation to it that is ascertainable, 



124 VITAL STATISTICS. 

viz., the number of births during the year; and in proportion to 
the deaths from the same disease at all ages. The percentages 
under the last heading give useful information as to the relative 
proportion of deaths from different causes occurring under one year 
of age; but they cannot be trusted beyond this. Thus a serious 
error would be caused by arguing that because 12-2 and 25*1 per 
cent, of the total fatal accidents at all ages in the male and female 
sex respectively occurred under one year of age, female infants 
were more subject to accident than male infants, the difference 
being caused by the fact that at higher ages females are much less 
subject to fatal accident than males. The real facts are in favour 
of female infants, only 2-9 out of every 1000 born dying under one 
year as the result of accident, Avhile 3"1 die among male infants. 

The largest producer of infantile mortality (atrophy, debility 
and inanition) evidently includes a large number of ill-defined 
conditions, many of Avhich are congenital. Diarrhoea will be 
considered later (p. 204). Convulsions again include diverse 
conditions, of which some at least are connected with parturition. 
This is indicated by the higher mortality from this cause among 
male infants, and by the fact that over 50 per cent, of the in- 
fantile deaths from convulsions occur under three months of age. 
It is remarkable that under so many heads there is an excess of 
male over female mortality. The only heading among the fifteen 
chief causes of infantile mortality tabulated on p. 125, under 
which female infantile mortality is higher than male, is whooping- 
cough (see opposite page). 

Accompanying the life-table in the Fifty-fourth Reiiort of the 
Registrar-General is a discussion of the facts relating to the chief 
causes of infantile mortality in England and Wales, 1889-91. 

In this report the causes of death of infants who die in the first 
year of life out of 100,000 live-born children are examined. The 
following features are seen to hold for both rural and urban 
experience. The excessive mortality of the first month is almost 
entirely due to premature birth, congenital malformations, and 
feeble vitality (atelectasis, atrophy, convulsions). Over four-fifths 
of the deaths in the first month are returned under these five 
headings. Diarrhoeal complaints reach their maximum destruc- 
tiveness in the third to the sixth month. Dentition appears as a 
cause of death oftenest in the last three months of the year. The 
comparative immunity from zymotic diseases of infants in the 
earliest months is very marked. Whooping-cough appears earliest. 
The deaths from measles do not become numerous until the eighth 



INFANTILE MORTALITY. 



125 



Deaths op Infants under One Year of Age, England 
AND- Wales, 1895, 



Causes of Death. 


No. of Deaths. 


Deaths under 1 year 
per 1000 Births of 


Deaths under 1 year 

per 1000 Deaths at 

all ages of 




Males. 


Females. 


Males. 


Females. 


Males. 


Females. 


Debility, Atrophj', 














Inanition 


11,755 


9,173 


25-1 


20-3 


93-3 


91-7 


Diarrhcpa, Dysentery 














and Cholera . 


10,554 


9,023 


22-5 


19-9 


73-3 


69-4 


Convulsions 


10,032 


6,812 


21-4 


16 6 


87-7 


78-8 


Premature Birth 


9,856 


7,649 


21-0 


16-9 


1000 


100-0 


Bronchitis 


8,966 


6,812 


190 


15-0 


36-0 


22-3 


Pneumonia 


5,187 


3,680 


11-1 


8-1 


25-6 


24-1 


Enteritis . 


3,649 


2,979 


7-8 


6-6 


64-8 


59-6 


AVhooping-cough 


2,119 


2,297 


4-5 


5-1 


49-6 


43-2 


Tabes Mesenterica . 


2,171 


1,684 


4-6 


37 


55-7 


48-4 


Ate] ectasis & Congeni- 














tal Malformations . 


1,832 


1,717 


3-9 


3 4 


95-5 


90-8 


Accident and Negli- 














gence 


1,474 


1,315 


3-1 


2-9 


12-2 


25-1 


Measles . 


1,414 


1,154 


3-0 


2-5 


24-1 


20-5 


Dentition 


1,380 


1,085 


2-9 


2-4 


59-8 


572 


Inilammation of Brain 














and Membranes 


1,361 


1,052 


2-9 


23 


33-9 


29-7 


Tubercular Meningitis 


1,211 


889 


2-6 


2-0 


32-8 


29-2 


All remaining Causes 


— 


— 


20-6 
176-2 


17-3 
144-3 


28-4 


23-5 




82,655 


65,438 



or ninth month. Scarlet fever scarcely makes its appearance in 
the first year of life. 

The mortality from diarrhoeal complaints is more than seven 
times, that from measles and scarlet fever is more than three 
times, as great in the town as in the country. Syphilis shows 
itself still more as an urban disease. Suffocation, mostly from 
overlaying in bed, and generally due to drunkenness, is also greatly 
in excess in towns. The mortality -from premature birth is nearly 
twice as high in the towns as in the rural counties. 



Factors of Infantile Mortality. Some of the causes of infantile 
mortality are common to every locality. Such are — 

(1) Prematurity of hirtli and congenital defects. The health 
conditions under which the mother lives have an undoubted 



126 



VITAL STATISTICS. 



influence on the vitality of her jDrogeny, and on the occurrence 
of i^remature birth. 

(2) Hereditary tendencies, such as the inheritance of syphilis, 
or degradation and drunkenness of parents, have also a very 
important influence. Some check on the marriage of unsuitable 
people has been suggested, securing the greatest good of the 
greatest number, and, in Dr. Farr's words, rendering "growth 
more perfect, decay less rapid, life more vigorous, and death more 
remote." The practicability of this is, however, more than 
doubtful. 

(3) The inexperience and neglect of mothers, especially of the 
industrial classes, is a most important factor in infantile mortality. 
As regards inexperience, it has been suggested that the deaths of 
first-born children should be separated from the general infantile 
mortality. Such returns would undoubtedly show that first-born 
children die at a higher rate than children of a later birth ; but 
some of the excess would be attributable to greater difficulty in 
parturition, as well as to parental inexperience. I^egiect on the 
part of parents is largely due to — 

(4) Industrial conditions. In the large centres of industry the 
employment of women in mills during pregnancy and at an early 
interval after childbirth has a deleterious effect on the welfare of 
their infants. The latter are sent out to nurse during the day, 
and commonly fed on farinaceous food, instead of milk. 

The following table suggests a partial but not a regular relation- 
ship between under-age marriages of women and a high infantile 
mortality. , 



Locality. 


In 1895. 


Out of 1000 

marriages tlie 

number occurring 

under 21 among 

women was 


The number of 

deaths of children 

under one year to 

1000 births was 


Staffordshire 

Nottinghamshire .... 
Derljyshire . . . . ' . 
West Riding i ,x , , . 
EastRiding°) Yorkslnre . . 

Durham ..... 
Northumberland .... 
Monmouthshire . . . 

England and Wales 


212 
2.37 
227 
203 
208 
244 
200 
245 

174 


176 
167 
149 
174 
187 
181 
166 
149 

161 



INFANTILE MORTALITY. 



127 



Dr. Geo. Reid, in a paper read l:)efore the British Medical Asso- 
ciation, 1892, gave the following statistics of infantile mortality 
in relation to the employment of married women in factories in 
Staffordshire. The population included in the statistics amounted 
to 438,712, and the statistics covered a period of ten years. Only 
towns having distinctly artisan jDopulations were included. The 
towns were then classified under three heads as shown below : — 



Staffordshire. 





Average Rates in Groups of Towns for 10 ) 


ears, 18S1-90. 




Deaths of 


Deaths from 


General 




Mean 


Cliildren 


Diarrhrea 


Death-rate 




Population. 


per 1000 


per 1000 


per 1000 of 






Births. 


Births. 


topulatiou. 


Class I. Many women 










engat,'ed in work 


112,078 


195 


28 


22-8 


Class II. Fewer women 










en<:;a^ed in work 


161,560 


16G 


20 


19-4 


Class III. Practically 










no women engaged 










in work . 


165,074 


152 


19 


18-1 



Although it is probable that other factors were co-ojierating, 
the preceding figvires seem to betoken a relationship between 
the factory employment of mothers and an excessive death-rate 
among their infants. There are, however, certain facts which- 
appear to indicate that female occupation is not the chief factor 
at work. Thus in the mining districts of Durham and South 
Wales, in which Avomen are not mvich engaged in industrial 
occupations, the infant mortality is higher than in the West 
Riding of Yorkshire, where many married women are employed 
in factories. Similarly the gradual increase in the number of 
premature Irirths has been ascrilied to the increasing industrial 
employment of women ; but the death-rate from premature births 
is higher in Norfolk and Suffolk, where only 20 per cent, of the 
women are engaged in some occupation, than in Lancashire and the 
West Riding of Yorkshire, where as high a proportion as 37 to 43 
per cent, of the women are thus employed (N. A, Humphreys). 

(5) Social position is closely related to industrial conditions 
in its intluence on infantile mortality. Thus in 1897 the infantile 
mortality per 1000 births ranged in London from 116 in Plum- 



128 VITAL STATISTICS. 

stead and 127 in Hampstead to 195 in St. Saviour's, and 197 in 
St. George's-in-the-East ; in the thirty-three great towns it ranged 
from 131 in Huddersfield to 262 in Preston; and in sixty-seven 
other large towns it ranged from 102 in Hornsey to 254 in 
Longton. Here we evidently have intermingled the effects on 
infantile vitality of social, industrial, and sanitary conditions of 
life. Farr''s Healthy Distrids Life-Table, based on the experience 
of sixty-three rural districts, showed an infantile death-rate of 103. 
Mr. C. Ansell (Statistics of Families in Upper and Professional 
Classes, 1874) found as the result of an inqiiiry relating to 49,099 
English children of the upper and professional classes, of whom 
2 per cent, were still-born, an infantile mortality of 80*5 per 1000 
born. 

(6) Improyer food and methods of feeding are responsible 
for a large share of infantile mortality. The improper substi- 
tution of farinaceous for milk food has been already mentioned. 
The use of uncleanly bottles containing milk in an incipient 
state of putrefaction is a common source of infantile diarrhoea. 
The close connection between methods of feeding and infantile 
mortality is shown by the fact that during the suiFerings and 
starvation connected with the siege of Paris in 1870-71, while 
the general mortality was doubled, that of infants is said to 
have been reduced by about 40 per cent., owing to mothers being 
obliged to suckle their infants. The same increase of adult and 
diminution of infant mortality was seen during the Lancashire 
cotton famine, when mothers Avere not at work at the mills. 
When improper feeding is a chief factor in producing infantile 
mortality, then a large proportion of the deaths are from diarrhoea 
and digestive diseases. Convulsions, again, are very commonly 
due to the irritation produced by improper food. 

(7) The deaths from accidental or homicidal violence require 
consideration. 

In 1895, 29 '6 per cent, of the total homicides in England and 
Wales (311), and 15-9 per cent, of the total accidental deaths 
(17,543) occurred among infants under one year of age. The 
infantile death-rate from accident and negligence was in the same 
year for males 3-1 per 1000 births, for females 2'9 per 1000 
births. The number of deaths of infants from suffocation in 
bed has increased from 124 per 1,000,000 births in 1885 to 174 
in 1890. Dr. Ogle found that these deaths occur chiefly on 
Saturday nights, the night on which there is the maximum 
amount of drunkenness. 



INFANTILE MORTALITY. 



129 



Influence of Age of Parents on Vitality of their Children. 

Dr. Matthews Duncan showed that the vitality of infants in a 
maternity hospital was greatest when the age of the mother AA'^as 
about 24 years. Kcirosi has investigated the same subject 
{7'ransactiuns of the International Congress of Hyrjiene aiid 
DeitHKjraphy, London, 1891, vol. x. p. 202) from the records at 
Ijudapcsth of the death of 29, (Si 3 children under ten years of age 
in relation to the age of their parents. Koriisi classifies the 
cause of death in these cliildren as " uterine," as premature Ijirth, 
Aveak constitution, and " extrauterine," where the cause of death 
is acquired after hirtli. 1 )iarrhofia is taken as the most impoi'tant 
instance of the latter. The general result is, that with the 
youngest mothers the numlier of weakly children is greatest. 
Tlie influence of the mother is shown in the following table : — 



Agfi of Mother. 


Out of 100 Deaths the cause of Death was 








Weakness or other 


DiarrlKva. 




Uterine Cause. 


Under 20 


57 5% 


26-3% 


20-30 . 


36-0% 


21-9% 


30-35 . 


26-9% 


18-1% 


Above 35 


28-8% ! 19-3% 




If tlie mortality 20-30 lie stated as 100, 




tbc foUowiiig table is obtained : 


Under 20 


158 


120 


20-30 . 


100 


100 


30-35 . 


77 


82 


Above 35 


82 


88 



On the father's side the youngest parents also appear to 
disadvantage. KiJrosi gives elaborate statistics bearing on the 
influence of the difl'erence of age and the condiined ages of 
the two parents. The general lessons confirm those taught l)y 
other considerations, viz., that girls should not marry before the 
age of 20, and that old men ought not to marry young women. 
Tlie inquiry is interesting, and it is unfortunate that the defective 
natal statistics in this country do not jiermit of its pursuit. It is 
particularly important tliat such statistics should be so classified 
as not to introduce the disturbing influence of social position. 



130 



VITAL STATISTICS. 



Infantile Mortality in different Countries. The following 
table from Eertillon {op. Hi., p. 83) gi\'es important data for 
ditferent European countries : — 







Tlie number ont of every 1000 
live-births 


Country. 


Period ol' 
Observation. 












Dying under one 


Dying (0-5) under 






J ear of age. 


live years of age. 


Ireland 


1865-83 


95 9 


164-6 


Norwaj' 


1866-82 


104-9 


179-1 


Scotland 


1865-81 


122-0 


230 9 


Sweden 


1866-82 


131-9 


222-5 


Denmark 


1870-82 


137-5 


204-9 


Belgium 


1867-83 


148-2 


253-2 


England and Wales 


1866-82 


149-2 


249-3 


Finland 


1878-80 


164-9 


— 


France .... 


1875-82 


]66-2 


251-1 


Switzerland . 


1869-80 


195-2 


266-3 


Prussia 


1874-82 


207-8 


316-2 


Italy .... 


1872-82 


209-7 


378-5 


Austria 


1866-83 


255-3 


389-9 


Russia in Europe . 


1867-78 


266-8 


422-9 


Bavaria- 


1866-83 


308-4 


393-2 



In jNIassachusetts in the twenty j^ears 1874-93, the infant 
mortality per 1000 births ranged between 172-0 (in 1875) and 
152-4 (in 1877), the mean being 161-9. 

In Hamburg, the mortality under one year old in the years 
1882-96 per 1000 living at this age, has ranged, from 201-9 in 
1894, to 368-8 in 1886. Eeference must be made to p. 80 for 
a caution as to the use of the above figures, owing to the varying 
significance of the term still-horn in ditierent countries. In 
England during 1891-95, the number of deaths under 5 years 
of "age per 1000 births was 228-9, while the infantile mortality 
was! 51 per 1000 births. 

Effect of Illegitimacy on Infantile Mortality. An examina- 
tion of Table 11, Ee(jUirar-GeneraVs Annual Bejyjrf, 1896, p. lii., 
does not shoAV any constant relation between the rate of illegitimacy 
and the entire infantile mortality in the ditferent English counties. 
Possibly a certain number of illegitimate births are in towns 
registered as legitimate, Avhile in rural districts they are correctly 



1802. 


1S03. 


1894. 


1895. 


189G. 


189' 


134 


158 


135 


151 


129 


13i 


360 


319 


173 


358 


233 


261 



INFANTILE MORTALITY. 1.31 

registered; a few illegitimate children again escape registration 
altogetlier. If, liowever, we separate tlie ])irtlis of legitimate and 
illegitimate cliildren, and adopt a like method foi' the corresponil- 
ing d(;at]is, tlie real facts are Ijrought to liglit. Tlie following 
figures for Brighton illustrate this point : — 

Deatlis of le<^itiniate infants 

per 1000 lc(,'itiniate births 
Deaths of illegitimate infants 

jier 1000 illegitimate births 

Thus an illegitimate child l)orn in Drighton during 1X97 had 
less than one-half the prospect of reaching the end of its first 
year of life which was enjoyed by a child Ijorn in wedlock. 

iJr. Farr summarized a large numljer of returns on the same 
subject as follows : — 

Number of deaths of Number of deaths of 

legitimate infants per illegitimate infants per 

_ , , 1000 legitimate births. 1000 illegitimate births. 

Twelve districts with a low 

infantile mortality . , 97 ... 388 

Twelve districts with a higli 

infantile mortality . . 192 ... 366 

In the face of such facts, the importance of illegitimacy as a 
national calamity is evident, and the following remarks, quoted by 
Dr. Farr from Von Bernoulli, are so apposite that we reproduce 
them here : " The invariable fact that the mortality among the 
illegitimate is far greater than among the legitimate, and that 
many more of them are still-born, shows clearly encmgh how 
much more unfavourable their position is from the first. Who can 
doubt that their bringing up is much harder and more difficult? 
that the existence of a class of men, bound to society by few or 
no !aiuily ties, is not a matter of indifference to the State 1 The 
great majority of foundlings are illegitimate, whicli of itself 
shows how little, as a general rule, the mothers can or will care 
for these children. It is beyond doubt that fewer illegitimate 
children grow up to maturity — that they get through the world 
with more trouble— than children born in wedlock, that more of 
them are poor, and that therefore more of them become criminals. 
Illegitimacy is in. itself an evil to a man ; and the State should 
seek to diminish the number of these births, and carefully inr^uire 
to Avhat circumstances any increase is to be ascribed." 

The necessity for regulations respecting illegitimate infants is 



132 VITAL STATISTICS. 

indicated by the significant fact that, according to Dr. Lankester's 
evidence in 1871, the inquests requiring to be held on illegitimate 
children under one year of age amounted to 31 per cent, of all the 
inquests held on infants, although such children formed less than 
5 per cent, of the total number of births. 

Such facts as the preceding led to the passing of the Infant 
Life Protection Act, 1892. 

This Act enacts that any person receiving for hire or reward more 
than one infant under the age of 5 years for the purpose of nursing 
such infants for a longer period than 48 hours, shall give immediate 
notice to the Local Authority, stating particulars as to age, sex, name, 
&c., of the children. Notice must also be given of the remoA'al of 
such children. It is the duty of every Local Authority to provide for 
the execution of this Act within its district, and for that purpose n^ay 
appoint inspectors to enforce the Act, for whom power of entry is 
given. It is the duty of the Local Authority to fix the number of 
infants under the age of 5 years wdio may be kept in any dAvelliug 
imder this Act. 

Any person keeping an infant under the age of 2 years, on con- 
sideration of a sum of money not exceeding £20 paid down, and 
without any agreement for further payment, shall give notice to this 
effect to the Local Authority. 

It is the duty of the Local Authority to give public notice of the 
ju'ovisions of this Act. 

When any infant coming within the terms of this Act is kept in 
any house so unfit or so overcrowded as to endanger its health, or is 
retained by any person who by reason of negligence, ignorance, or 
other cause is so unfit to have its care as to endanger its health, any 
person appointed for the purposes of this Act may apply to the Local 
Authority for an order directing him to remove the infant to a work- 
house or place of safety. 

An inquest must be held in case of the death of any infant 
respecting whom notice is required under this Act. 

Insurance of Infants in Relation to Infantile Mortality. 

Much evidence has been published on this subject, which has 
both statistical and social interest. In England, in 1890, there 
were 4,150,000 children under 10 years of age insured, such 
insurance, especially for infants, being general among the indus- 
trial classes. The maximum sum which is legally payable on the 
death of a child under 5 years is £5 ; the maximum sum in the 
case of a child under 10 years is £10. The matter has been 
frequently revised from the legislative standpoint. The Friendly 
Societies Act of 1829 allowed minors to become members. The 



INFANTILE INfORTALITY. 133 

Act of 1846 limited tlie insurance to those over 6 years of age. 
After an investigation by a Committee of the House of Commons, 
in 1849, the Act of 1846 was altered in 1850, it being rendered 
laAvful to assure on the death of a child under the age of 10 years 
to the extent of actual funeral expenses, })ayment of which must 
he made to the undertaker direct. In 1854 the amount that 
could he paid on a child's death was again enlarged. In 1875, 
after further investigation, the Act was still furtlier ])roadened, so 
as to allow of the insurance on children under 10 years of age 
being paid to the parents. A more recent Parliamentary inquiry 
reported, in 1891, that they did not consider further legislation 
necessary. 

The Prudential Assurance Comjiany have a table based on the 
experience of nine million insured lives, with which they contrast 
the experience of Farr's English Life-Table. The relative infantile 
mortality in the two is 99'5 and 165"5. As the insurance expe- 
rience almost certainly does not include many new-born infants, it 
is proposed to omit the first month's deatlis from the English 
figures. When this is done, they become 108, as against the 
Prudential 99 "S. At ages one to two the respective death-rates, 
according to English and the Prudential Society's experience, are 
65-6 and 632; two to three, 36-1 and 32'4 ; three to four, 24-3 
and 18"6 ; four to five, 17"9 and 13*5 ; five to six, 13"5 and lO'O ; 
six to seven, 10'7 and 7"6 ; seven to eight, 9-16 and 5*7 ; eight to 
nine, 7"7 and 4*9 ; nine to ten, 6 '6 and 4'3. 

There are other similar statistics, and it appears fairly clear 
that after free allowance for selection of insured lives, and for 
the fallacies connected with the extremely high mortality soon 
after birth, there is no trustworthy statistical evidence of the ill 
eliect on the life-prospects of children from life insurance. There 
is no proof that neglect and crime have been greater in their 
incidence upon insured children, and it can scarcely be held that 
the prospective receipt of insurance money has been the incentive 
to child neglect and child murder in more than a very small number 
of cases. 

Relation between Birth-rate and Infantile Mortality. The 

infantile deaths being stated in their ratio to the infantile 
population, or the nearest api)roximation to it — in the number 
of births — that can be ascertained, it is evident that the number 
of deaths under one year will necessarily increase Avith the 
number of births. There is, however, nothing in this^ to imply 



134 VITAL STATISTICS. 

that the infantile death-rate should be increased by a higher 
birth-rate. Dr. H. -R. Jones {Jowr. Statist. Soc, vol. Ivii. part i.) 
has foiTnd a local connection in northern towns between a high 
birth-rate and a high infantile death-rate, as shown in the 
following table : — 

Northern Towns, 1871-80. 



Birth-rate. Kate of Infantile Mortality. 



Over 35 
Under 35 



168 
144 



The association is by no means regular, nor do we consider 
it inevitable. If the birth-rates and the infantile death-rates 
in the thirty-three great towns in 1897 be analyzed, the ten 
towns with the highest birth-rates are Gateshead, 35"1; Liverpool, 
35-3; Wolverhampton and Salford, 35-1; Sunderland, 34'6 ; 
Sheffield, 34-4; Hull, 33-4 3 Birmingham, 33-3; Manchester, 
33 "2; and West Ham, 32"2. The ten toAvns with the highest 
infantile death-rates were Preston, 262 ; Burnley, 220 ; Salford, 
219; Wolverhampton, 217; Birmingham, 214; IS'ottingham and 
Blackburn, 206; Leicester, 205; Liverpool, 200 _; Sheffield, 198. 
Thus five appearing in the last list do not appear in the first. 

There is nothing surprising in the frequent association of a 
high birth-rate and a high rate of infantile mortality. The 
highest birth-rates usually occur in crowded industi-ial towns, 
in which the evil effects of industrial occupation of married 
women are commonly associated with those, of intemperance, 
ignorance, and neglect, with all that these factors imply. 

A high degree of density of population is not necessarily 
associated Avith a heavy infantile death-rate. Thus I have shown 
(Jour. Statist. Soc, March, 1891) that in the Peabody Buildings 
having an average density of 751 persons to an acre, as compared 
with 58 persons to an acre in the whole of London, there was 
infantile mortality averaging 139 in the nine years 1882-90, 
as compared with 152 for the Avhole of London. Increased 
density of population, however, commonly carries with it other 
evils. "The direct consequences of close aggregation" (liability 
to fouling of the air, the soil, and often the water, and the more 
easy spread of infectious diseases) "are probably as nothing in 



INFANTILE :\rORTALITY. 135 

comparison witli its indirect consequences or conconiitaiits. The 
more crowded a community, the greater, speaking generally, is the 
amount of abject want, of filth, of crime, of drunkenness, and of 
other excesses, the more keen is the competition, and the more 
feverish and exhausting the conditions of life. Moreover, and 
perhaps more than all, it is in these crowded communities tliat 
almost all the most dangerous and unhealthy industries are carried 
on. It is not so much the aggregation itself as these other factors 
which are associated with aggregation, that produce the high 
mortality of our great towns or other thickly populated areas." 
(Siqijdeinent to Forty-fifth Annual Report of the Reyidrar-General, 
p. xxi.) The effect of unhealthy industries is only felt indirectly 
by the infantile population ; but, apart from this, the above 
remarks explain clearly why great density of population and the 
liigh birth-rate commonly accompanying it are usually associated 
with a high rate of infantile mortality. 

The following remarks from my paper on " The Vital Statistics 
of Peabody Buildings," appear to me to state the true relationship 
between a high death-rate, especially a high infantile death-rate, 
and density of population. 

"The number of rooms occupied by each family is of much 
greater importance in relation to healtli than the number of 
persons living on a given acre, as this fact throws important light 
on the state of each tenement as regards overcrowding. In the 
Peabody Buildings the average number of persons to eacli room 
is 1"8. Given houses properly constructed and drained, and given 
cleanly habits on the part of the tenants, increased aggregation of 
population on a given area has no influence in raising the death-rate, 
except in so far as it is accompanied by overrrorrdiiKj in individual 
rooijift, an event which is l)y no means necessary under tlie circum- 
stances named. In other words, there is no causal relationship 
between density of population ^>fr t^e and a high mortality. The 
true index of density is the number of persons to each occupied 
room." 



CHAPTEE XV. 

INFLUENCE OF CLIMATIC AND SOCIAL CONDITIONS 
ON MORTALITY. 

Wp] have in the last two chapters discussed the effect of varying 
age and sex-distvibution on the general death-rate, and on 
the death-rate at different age-groups. Before considering the 
mortality from special diseases, the influence of climatic and social 
conditions, of density of population, and occupation, require 
attention, and to these the present and two subsequent chapters 
will be devoted. 

The influence of climate can only be separated with difficulty 
from that of other conditions of environment. To obtain trust- 
worthy statistics under this head, it would be necessary to eliminate 
the effect of variations in the age-distribution of the populations 
compared, of density of population, staple industries, and of 
differences in food and in other particulars. The Army Reports 
for different foreign and home stations are a most promising field 
of investigation in this connection, if the necessary precautions 
above indicated are taken. It is well in investigations concerning 
climate to consider separately its effect on strangers and on the 
indigenous inhabitants. 

Many important facts as to the connection between climate and 
disease can be statistically elucidated, as the varying amount of 
malaria, the endemic and epidemic prevalence of cholera, the 
localized distribution of yelloAv fever and leprosy, the almost 
complete alisence of diphtheria from tropical regions, * and so on. 

Season has an influence which can easily be stated in figures. 
It is customary to separate the death-rates from all causes and 
from different diseases according to the quarter of the year. 

* See Epidemic Diphtheria, by the Author, p. 152. - 
136 



CLIMATIC AND SOCIAL CONDITIONS. 



137 



Anotlicr plan, presenting some advantages, is to divide tlie numT)er 
of cases of, or deaths from, a disease into those occurring in tlie 
winter — December to February, in the spring, ]\Iarch to JNIay, in 
the summer, June to August, and in the autumn, Sej^tember to 
November. It is often useful also to state the number of cases 
or deaths for each month of the year. When this is done the 
object, presumably, is to give the relative incidence of the disease 
in each month, and for this purpose a correction is required for 
the varying lengths of the months. The following example is 
taken from Dr. Abbott's report {Ticeutij-sLrtli Aimual Report, State 
Board of Health, Mas-sachuaetts). 

Mortality by Months, Massachusetts, 1893. 





Total Deaths ia 

Moutli. 


Montlily Deaths 

reduced to a 
Standard of 100. 


Deaths per day. 


January 

February 

Slarcli .... 

April .... 

May .... 

June .... 

July .... 

August .... 

September 

October 

November 

December 


4161 
3714 
4375 
4335 
4321 
3250 
4.356 
4934 
4055 
3679 
3480 
4424 


99-8 

98-6 

104-9 

107-4 

103-6 

80-5 

104-5 

118-4 

100-5 

88-3 

86-3 

106-1 


134-2 
132-6 
141-1 
144-5 
139-4 
108-3 
140-5 
159-2 
1352 
118-7 
116-0 
142-7 


49084 


100 


134-5 



The standard month is assumed to contain 31 days. The 

49084 X 31 
average number of deaths in 31 days = .^^ =4169. 

But in January 4161 deatlis occurred in 31 days. 

4161x100 
Therefore the deaths in this month were — jTro = 99-8 

per cent of the standard. 

Similarly for February, first find what would have lieen the 

numljer of deaths had this month had 31 days in it. 

5Iii^ = 4113 
28 



138 



VITAL STATISTICS. 



Then the deaths in the second month of 31 days were 

4112x100 ^^^ 

— TTFq = 98'6 per cent of the standard. 

And so on for the other months. 

From 1886 to 1896 inckisive, the death-rate in England has 
always been highest in the first quarter of the year, with the 
exception of 1891, in which it was higher in the second quarter 
(23 "7 as compared with 22 0), 1893, in which it was higher in 
the fourth quarter (19*9 as compared with 19'7), and 1896, in 
which the deatli-rate in both the first and fourth quarters of the 
year was 17*9. The third quarter usually has the lowest death- 



J(W. Feb Mar Apr. May •June 'July Aii^- Si pi Oc" t^nv. Dec^ 




Fig. 9. 
Seasonal Incidence of Deaths from all causes in London (50 years, 1841-90). 



rate. In 1886-96 it was lowest in this quarter, except in 1893, 
when it was lower in the second quarter (18"0 as compared with 
19 "2); in 1895, when it was also loAver in the second quarter (17'2 
as compared with 17 "5); and in 1896, in which both the death- 
rates in the second and third quarters was 16 "3. In the years 
1838-95 the English death-rate for the first quarter averaged 
23-8, for the second 21*0, for the third 19 "5, and for the fourth 
21"0 per 1000 per anniim. The low mortality in the third 
quarter of the year would be still more marked but for the 
prevalence of Epidemic Diarrhoea. 

Mild Avinters and cool summers both lower the mortality, the 
former especially of the old, the latter of the young, and 
especially of the infantile population. A cold, wet summer is 
always accompanied by a low mortality. The effect of an ex- 
cessively cold winter and of a cool summer on the weekly 



CLIMATIC AND SOCIAL C0N1)ITI0X8. 139 



,la/v J-'cb. Mai: 


Afrr. May Jutj^ <^''^y -^"^ ScpL 


Oct Nov. Dec 




i 














^ 






























'^ 




^ ■'^ i"^ 




1 "'''• 






!<,: ^'■ 


____T 




I V ^ 


1 




__4-^-^i 


^ " " ":^-:::= 


Ll 


/ i ^^g 




tt II 1 








Y 




i::::::::::::::::T::i:::: 






^ t . 


::: i: ^it 




:i...... i..i— ■ 




















i. . _ 






' 




::::\::::::::::::::::::::::: 












^ ^ 


1 




5 I 


:r^t ■ 




^ :::\-:4::^;- 


ii.i:::r:: 




L t.\ 






\ ,._ ,.!._._ 


ff:5""":" '*' 




t , \ 


t 4i it 




_ _ _-5 _ L_ _ 


.4-- -^ 




^_. 1 ._ 


1 




s,.t .___,__ 


1 T 




_ __ J.._ /. 






... % ^ ' /.. 






>-~,y 












i 1 


1 ~r 




it'-'"- \" 






.._ t- 






. _ ... ... k 






] 


-l- - -_ - 




.... . , I 






ti ' '" 


v:::::::::: ^ 




7 


-A 




^ 


- S.. 




. , ,. ■' 






J. 


± 



Fig. 10. 

Seasonal Incidence of Deaths from Diseases of the Respiratory Or<,'ans and 
from Diarrhcea in London (50 years, 1841-90). 



mortality in London at all age.s, at ages over 60, and under one 
year of age respectively, may be seen by plotting out the deaths 
under these tliree heads diagrammatically. The figures for this 



uo 



VITAL STATISTICS. 



purpose can be obtained from the weekly returns of the Eegistrar- 
General. If the period 1890-91 be taken, the returns show the 
effect of the intrusion of an additional cause of mortality — influ- 
enza — April to June. The diagram may be commenced with the 
week ending November 8th, 1890, in order to illustrate the eff'ect 



Jan. Feh M a r. Apr. May Jt /ne/ July Av^. Sept . Oct. Nor. Sec. 




*SOperctnt 



The nwan line npresents an. nyerage wprUy vianber of 17 dMoths 

Fig. 11. 
Seasonal Incidence of Deaths from Small-pox (50 years, 1841-90). 

on total deaths and deaths over 60 of the exceptionally excessive 
cold which occurred between Novemljer 25t]i and January 22nd. 
Between ISTovember 25th and December 31st the average 
deficiency of the mean daily temperature was 11° "4 Fahr., being 
as much as 21°"4 below the average on November 28th, and 
2r-0 below on December 22nd. In the first 22 days of January 



July -Auf). Sept. Oct. Hor. Dec. 



MF.AN LINE- 



-(SlOJpo-cwi/ 




^SOjxrcoit 



6Vpercf*-'- 



The mean, luui represents an.ay<crage weekly mimbi-r of ST-aJnusswn." 

Fig. 12. 

Seasonal Incidence of Admissions of Small-pox Patients to Metropolitan 
Hospitals (15 years, 1876-80). 



CLIMATIC AND SOCIAL CONDITIONS. 



141 



tlio me.an daily deficiency of temperature from tlie average was 
7°"9, the greatest deficiency being 18°'7 on the 10th. The effect 
of this protracted and exceptional cold is seen in the curve of 
total deaths, and particularly in that of persons over GO, very 





Mar Apr May June 


July A 


iLo. Sept'. Oct Nov Dec. 


-.^^-;=: - 


:t:" 


:::::~ 


:::::::::;::: 


io 


fu_^'^ -i^ 


■■-: -t-^i- 


:; \\ 


■ - - : 


- 


~w 




' ::: ^:':j:.__ ._ 









_: 'MEAN UNK 


30 f 

30 


-_: : 


^, 


-:::::_ ::;: - 




"SO percent- 1 1 1 ' 1 — 1— 1_J_1- 


----' ---- F ^ 


'-'-- 


iXLL 


fflSffit 


J. 1 J i 1 .1X1 — — 60p«rc4r\t 



Ihe mean, lute represents on ateraqe weekly number of-*7 ileuOis 

Fig. 13. 

Sea.sonal Incidence of Deaths from Wlioopinif-coiigh in London 
(50 years, 1841-90). 

slightly in the curve of deaths of infants. In A]-)ril a new 
cause of excessive mortality, viz., influenza, intruded itself. The 
official figures do not sutliciently show the true share of influenza 
in this excessive mortality, as deaths from bronchitis and 



'SOper 



•Jan. B^b. Mar. Apr. May June. July. Aug. SepL Oct. Ifdv. Peo. ^ 




The mt'im line rfprr.rfnia (uv uyerag^' weekly number of 34 <iaiths 

Fig. 14. 
Seasonal Incidence of Deatlis from Measles in London (50 years, 1841-99). 



imeumonia were also very excessive, and had a common origin 
in influenza. The rise in mortality in August was unusually 
small in extent. It was almost (mtirely confined to infantile 
life, and was caused by diarrhoea. The exi)lanation of the small 
amount of diarrhea in the summer of 1891 lies in the fact that 



142 



VITAL STATISTICS. 



the mean temperature was below the average from July 1st to 
September 7th, on August 6th as much as 9° "5 below. 

Season has, it will be seen, an important influence on the 
character of prevalent diseases, intestinal diseases being most 
prevalent in summer, and respiratory diseases in winter. 



Jcav. Feb. Mar. Apr. May June- July Aun. Sent. 


Oct. Mjv. Dec. 




-+t::— -±-'±-::: + :::: 


-I'- "'s : so 










" ~ - _ - 


40 
























- r JV 




" < 














































^ . : : . i , 












•'^ - - -"'r 


<,_,-."'"!.i V---- ---. 




10 ■" 
























- eovercenb — 1 M 1 1 1 1 1 1 1 M 1 




1 ' 1 1 1 1 1 1 ' 1 1 1 1 1 eOpercep' 



JTie ifufxn- line r&presents a/v cwera0& weekiy numi?0r of 4^ dea^is. 

Fig. 15. 

Seasonal Incidence of Deaths from Scarlet Fever in London 
(30 years, 1861-90). 

The following curves, taken from the Annual Summary of the 
Registrar-General, 1890, illustrate very clearly the seasonal inci- 
dence of general mortality and of the mortality and prevalence 
of certain diseases. 





TeiJ. Mar. 


AXT 


May 


Jiiru. 


July 


Axuj. 


Sept. Oct Nov. Ueo. 
























































































(is. ' 


















































































































































































































i -'- - 






























f 
































































70 'X 




-- 


-" 






-' 


- 




- 


--- 


-- 


¥' 











r" 


"r 






"~ 


r 




Z 




'z 


i-z 




#m#r 








































































f\ 






















_5 








y 


































































































































































































































































































~80 per cent 


, . 











__ 


_ 




_ 




_ 




1 





The mean Uiie represents an. ayenxrje weekly luimlvr of 55 aAmssUta. 

Fig. 16. 

Seasonal Incidence of Admissions of Scarlet Fever Patients to Metropolitan 
Fever Hospitals (16 years, 1875-90). 



CLIMATIC AND SOCIAL CONDITIONS. 



143 



Figs. 9 and 10, relating to "Deaths from all Causes" and 
" Deaths from Diseases of the Respiratory Organs " and from 
"Diarrlioea," show the actual average deaths each week. In 
these diagrams the thick horizontal line represents the weekly 
mortahty from the disease to whicli the diagram relates, the 
iifty-tliird week, whan it occurs, being ignored. The curved line 
I'epresents the amount per cent, by which the average mortality 
in each week differs from this mean, above or below it. The 
length of experience taken as the basis is stated in' each instance ; 
usually it is 50 years. Some allowance must be made for the 
facts that the curves are formed on the deaths registered in each 
week, registration usually occurring a few days after death, and 
that the curves relate to deaths, the end of each fatal attack, not 



, ,_ _ Jan Teh. Har. Apr. Mm June 


Julf AU0. Sept Oct. Jfcv Dec 








-: ;: — :-:: = :--5- 
















__ - _^ '^ii 


























:<. '" 


lO — -- 


1. ti-J It 


::::_-ii:"5s:;;t-'r:-±: 


w 


MEAN LINE — .^ 


-;f5; -3-^-4-^-------^ 


i^-~Cf^-^~~-:^'—^-^ 




w — 5 






10 


3i> ^Vi 


ffwflflffffr 1 v\ 


:::::4:::::-:::::::::ti 


2^ 


10 i\ 

—dOpcrcent — tjl 


iiE:i::EE;::::i:.::i: 


\mMmk^ 


W 

"^—BOpcrcera. 



The iiuan line represents an avcnuie- wcelily number of >Z deaths 

Fig. 17. 

Seasonal Incidence of Deaths from Diphtheria in London 
(30 years, 1861-90). 



the date of attack. Furthermore, the fatality (case-mortality) 
of certain diseases varies according to season. For this. reason 
curves of weekly admissions of any of the diseases which are 
treated on a large scale in public hospitals are also given. 
Allowance must be made in the curves of weekly admissions 
for the fact that, unless a long series of years is taken, the 
chance fluctuation caused by an unusually large epidemic occur- 
ring possibly at an unusual season disturbs the symmetry of the 
curve. The following remarks in the Annual Summary of the 
Regisirar-General, 1890, so clearly bring out the chief points of 
interest in the ditierent curves, that they are reproduced : — 

"It is of interest to compare the admission curves (Figs. 12, 
16, 19) with the corresponding mortality curves (Figs. 11, 15, 18). 
We should anticipate that, as the former relate to the commence- 



144 



VITAL STATISTICS. 



ments of the attacks and the latter to their terminations when 
fatal, the maximum and minimum points in the former would 
precede the maximum and minimum points in the latter ; and 
to a certain extent, though not quite so decidedly as might be 
expected, this is the case. We should also expect that the 
seasonal differences in the admission curves would be more 



Jan.'. Feb. Mar Apr. May Jma July Aug. Sept. Oct. Nov Dec 
+ ^percent — , , [ , , , , , , , , , |- , , | , , , | , | | - p| | | i | | | | | " f | | | | | _r TT fl ! i»f ! ^ i III' — ^SOpa-cent 



iiP 



i: 



The meofv Une represents an, average weekly ruuniier of IS deaOis. 

Fig. 18. 

Seasonal Incidence of Deaths from Enteric Fever in London 
(22 years, 1869-90). 



strongly marked than in the death curves ; for the deaths that 
occur among the attacks of a given Aveek will not all occur in one 
other later week, but Avill occur gradually and be spread over 
several successive Aveeks; so that while the number of attacks 
in a given week will be represented by a single point, the deaths 
corresponding to those attacks will be represented by a more or 
less extended line, uniting successive points in several weeks, the 
number of which will depend upon the duration of the disease. 
The death curves, in short, should be flattened out in comparison 
with the admission curves, and the flattening should be greater 
the longer the usual duration of the disease. An examination 
of the curves shows that this anticipation is fulfilled. The three 
mortality curves are all more or less flattened as compared with 
the admission curves ; and the flattening is greatest in the enteric 
fever curve, the average duration of this disease being the 
longest, and is least in the scarlet fever curve, in Avhich disease 
the average duration is the shortest. 

"This comparison gives us a notion of the changes that we 
must make in the mortality curves of the other diseases, in order 
to make them more closely represent the curves of seasonal pre- 



CLDIATIC AND SOCIAL CONDITIONS. 



U5 



valence. We must push the curves somewhat further ])ack, so as 
to make maximum and minimum come respectively at a somewhat 
earlier date ; and we must raise this maximum and lower this 
minimum to an extent determined by the number of weeks 
through which fatal attacks of the disease with whose curves 
we are dealing may extend. 

" Tlie curves tell their own story suiticiently distinctly to make 
it unnecessary to describe them severally in detail. They may, 



(?<* Nov. Dec. 



*110perca^ 




Op^rcerdb 



MEAN LINE 



-aOpiy'OTttr 



-SOperceni, 



Thj:. miiif! Zma represent an, average, weekfy numier <ff9 admisShons 

Fig. 19. 

Seasonal Incidence of Admissions of Enteric Fever Patients to MetropoUtan 
Fever Hospitals (16 years, 18?5-90). 



however, for convenience be classed in groups, according as the 
curve consists of a single or a double annual wave, and according 
to the periods of the year in which the wave or waves reach their 
highest and lowest points. The curves for diarrhoea and for 
diseases of the respiratory organs (Fig. 10) are distinctly single 
waves, the former with its crest in the summer, the latter in the 
Avinter ; and it is the combination of these two very marked 
seasonal curves that mainly determines the double Avave outline 
of the curve (Fig. 9) of mortality from all causes. The curves 
for scarlet fever (Figs. 15 and IG), diphtheria (Fig. 17), and 
enteric fever (Figs. 18 and 19), are also single wave curves, 



146 VITAL STATISTICS. 

closely resembling each other, in that in each of them the wave 
rises to its crest in October and November, while the trough 
extends from February to August. In strong contrast with this 
group are the curves of small-pox (Figs. 11 and 12), and of 
whooping-cough (Fig. 13), which cover with their crests January 
to June, while their troughs extend over the rest of the year. 
These curves, moreover, show some tendency to consist of two 
waves, for in each there is a slight but, nevertheless, distinct 
depression in the months of February and March. There remains 
the curve of measles (Fig. 14), Avhich consists unmistakably of 
two Avaves, having their crests respectively in June and in 
December, while they fall to their lowest levels in February and 
September. 

"The effects of small-pox and whooping-cough upon the 
general seasonal mortality are practically effaced by the almost 
exactly contrary effects of scarlet fever, diphtheria, and enteric 
fever ; and thus the general outline of the curve of mortality 
from all causes (Fig. 19) is mainly determined, so far as the 
diseases noAV considered affect it, by a combination of the curves 
for diseases of the respiratory organs, for diarrhoea, and, in a 
lesser degree, for measles." 

Cyclical Changes. The fact that certain diseases, especially 
those of an infectious character, recur after an interval of years, 
shows that, apart from the influence of the season of year, there 
are periods of change which require for their comj)letion a series 
of years. Mr. Netten Radcliffe has drawn attention to the fact 
that the law of periodicity of epidemic and pandemic diseases is 
not yet determined. Two factors appear to be at work : (1) the 
influence of an accumulation of susceptible persons in the intervals 
betAveen two epidemics of the same disease ; and (2) certain 
extraneous conditions which appear to be operative in determining 
the periodicity, but about which little is knoAvn. The first factor 
is exemplified hj the fluctuations in the amount of small-pox in 
England, AAdiich have been observed to have a close relationship 
Avith the fluctuations in the number of unA^accinated children — a 
relationship so close that the periods of recurrence of epidemic 
small-pox could be pretty accurately forecasted. The second 
factor appears to be exemplified by the fact that, in 1871, when 
one of the periods of epidemic increase Avas due, some other 
undetermined condition gave to the epidemic of 1871-72 a severe 
character not observed in small-pox since the general introduction 



CLIMATIC AND SOCIAL CpNDITIONS. 147 

of vaccination. ]\Ir. Radcliffe gives as other instances of a similar 
character the great epidemic of sypliihs in tlie fifteenth century ; 
the exceptional develo})ment of fatal diarrhoea in this century ; 
the great development of di))htheria within the last thirty years ; 
and the appearance within recent years of cerehro-spinal fever ; 
which he regards as evidences of secular-pathological changes, to 
which a clue must be sought l^y studying their relation with 
secular meteorological and telluric changes. The solution of the 
prol)lem Avhy cholera is now endemic in India, then becomes 
epidemic, and finally pandemic at intervals, belongs to the same 
category. 

Since the above was written rheumatic fever (IMilroy 
Lectures, Lawet, INlarch, 1893) and diphtheria {Epidemic Diph- 
theria : a liesearrh on the Oriijin and Spread of the Disease from, 
an International Standpoint, Swan Sonnenschein & Co., 1898) 
have been made the subject of a very detailed international study 
by the author. The result, particularly in the case of diphtheria, 
has been, it is believed, to elucidate the conditions determining 
the cycles of prevalence of the disease ; and to prove that both 
diphtheria and rheumatic fever occur in epidemics almost ex- 
clusively under meteorological and telluric conditions wliich are 
very remote from those supposed by most medical men to lie 
commonly associated with these diseases. 

Effect of Race. The table on p. 16 shows the death-rate in 
ditferent countries; it is obvious, however, that other causes of 
ditference are at work in addition to race, and that correction is 
required for differences of age and sex-distribution. 

Mr. Hoffman's treatise on Race Traits and Tendencies of the 
American Negro (1896, Publications of the American Economic 
Association) contains valuable statistics as to the vital differences 
between the white and coloured population in the States, based in 
part on the census report of 1890. Thus the combined experience 
of ten southern cities, 1890-94 (including Washington, Baltimore, 
and New Orleans) shows a death-rate among the white of 20"1, 
among the coloured population of 32 '6, notwithstanding the fact 
that the age-distribution of the coloured is shown by the census 
returns to be far more favourable to a low general death-rate than 
that of the Avhite population. These rates are based on populations 
of over 5 and 2 millions respectively. The following further 
death-rates may be quoted. 



148 



VITAL STATISTICS. 



Death-rates of Baltimore and Washington, D.C, for 1890, 
PER 1000 Living at each Age-group. 





Baltimore, Md. 


Washington, D.C. 


Ages. 


White. ' 


Coloured. 


White. Coloured 


Under 5 years 


. 80-3 . 


.. 171-8 


65-0 ... 159-3 


,. 15 ,, 


. 30-7 . 


64-2 


23-9 ... 57 


15-45 


. 9-0 . 


14-9 


9-3 ... 17-1 


45 years and over 


37 "5 


.. 42-3 


33-9 ... 47-6 



The percentage of excess of negro mortality is highest for the 
period of life under 15. Mr. Hotiman brings forAvard evidence 
to show that this is due more to race degeneration than to the 
fact that the environment of the coloured is Avorse than that of 
the Avhite population. In the Northern States the coloured race 
does not hold its own, the deaths outnumbering the births ; the 
apparent increase of the coloured population is due exclusively to 
migration. INlr. Hoffman shows also that the mortality in the 
coloured race is increasing, while that among whites is on the 
decline. 

Medical experience in the war between the North and .the 
South proved that the adult negro male was more subject to 
malarial disease than the white soldier, the rate of admissions to 
hospitals for malarial diseases being 522 per 1000 for the Avhite 
troops, and 829 for the coloured troops ; while the average death- 
rate in the tAvo classes AA'as 3-36 and 1003 per 1000 respectively. 

The excessive death-rate among negroes is caused chiefly by 
excessive infantile mortality, phthisis, pneumonia, scrofula, and 
A^enereal diseases. 

In the year of the 1890 census, in American cities of 100,000 
jxipidation and upAvards, the folloAving death-rates per 1000 of 
each population occurred, the deaths being classified accord iiiii to 
the hirtli-place of the mother : 



United States 


. 20-87 


Canada 




19-61 


England 


ind Wales 


. 19-38 


ScandinaA-ia 




19-04 


Ireland 




. 26-74 


Bohemia 




2719 


Scotland 




. 19-16 


Italy . 




33-35 


France . 




. 19-00 


Otlier foreign 


conntries . 


23-74 


Germany 




. 19-87 









Part I. of the United States Eleventh Cenms Bejwrt for 1891, 
"Vital Statistics," p. 38 et $eq., contains a number of further 
statistics bearinsa: on race. 



CLIMATIC AND SOCIAL CONDITIONS. 149 

Effect of Marital Condition. The table on p. 62 shows at 
tlic time of the census 1891 that the proportion of unmarried in 
the EngHsh })Oi)ulation diminished with each successive age-period. 
" Afi regards the earlier age-periods, tliis is readily intelKgible, 
because marriage, as well as death, tliins the ranks of the single 
until marriage-age is? past." The persistent weeding out of the 
Ijachelors and spinsters, even in advanced life, can, however, so 
far as can be seen, be only explained l)y supposing that their rate 
of mortaHty is higher than that of married persons of similar 
ages. One would have anticipated that the weeding out of those 
Avho remain single, because unfit for matrimony, would have 
become complete before, say, the age of 55 ; and tlie fact that this 
is not so, lends itself to the view that married life is more 
favourable to longevity tlian celibacy. 

The same conclusion is favoured by the results of the United 
States census, 1890, which should be consulted for iiarticulars. 

Effect of Sanitation. Uetween 1851 and 1871 the towns of 
England increased from 580 to 938, their population from nine to 
fourteen millions; but notwithstanding the tendency of greater 
density of population to be associated with an increased death-rate, 
the death-rate remained practically stationary. Since that time 
there has been a remarkable reduction in the death-rate, concerning 
which we cannot do better than quote the Registrar-General's 
Report for 1881 (p. xv. et seq.). "There is nothing in the series 
of annual reports issued by this office that comes out more dis- 
tinctly and unmistakably than the wonderful eliect which the 
sanitary o[)erations of the last decade have had in saving life. 
The Public Health Act came into operation in 1872. The average 
annual death-rate for the immediately preceding ten years (1862-71) 
had been 22'6, and there were no indications whatsoever of any 
tendency of the rate to fall lower. Indeed, in 1871, the final year 
of this period, the rate Avas exactly the average, viz., 2 2 "6. The 
Act came into force, and at once the rate began to fall, and con- 
tinued to fall year by year with almost unbroken regularity, until 
in 1881 it was no more than 18*9. Once only in the ten years 
that had elapsed since the Act came into operation was the rate as 
high as the average of the })revious decade. That was in 1875, 
when the rate was 22"7. In that year a second Public Health Act, 
of more stringent character, came into operation ; and from that 
date down to 1881 the death-rate did not once reach 22*0, and 
averaged no more than 20'5. 



150 VITAL STATISTICS. 

" Had the fall in the death-rate l)een limited to a single year, 
or to two years, or even to three, it might have been argued by 
sceptical persons that the improvement was due to a succession 
of seasons favourable to health, or to other causes unconnected 
Avith sanitary administration, and that the setting in of the fall 
coincidently with the coming into operation of public health 
measures was no more than casual ; but in face of a fall, lasting 
for ten years in succession, and increasing each year in amount, 
no one can seriously maintain such a position. There can be no 
real doubt that the saving effected in life was the direct product 
of the money and labour expended in sanitary improvements. 
Doubtless the money thus expended was enormous in amount ; 
and it Avill be well, therefore, to consider what return it has 
brought in. If, then, the death-rate in 1881 had been only equal 
to the average death-rate in the decade preceding the Public 
Health Act of 1872, there would have died in the course of that 
one year 96,917 persons who, as it was, survived. From this 
total, however, a deduction must be made of some 5000 for the 
following reason : — The birth-rate in 1881 and in each of the two 
immediately preceding years was considerably below the average 
annual birth-rate in 1862-71. Consequently there was a smaller 
than average proportion of children in the first three years of life 
in the population of 1881. But the death-rate at this early period 
of life is always very high. Had the birth-rate in 1879, 1880, 
1881, been equal to the average birth-rate in 1862-71, there 
would have been so many more young children living in 1881 as 
to have increased the deaths in that year by a number close upon 
5000. Instead, therefore, of 96,917 lives saved, we have only 
about 92,000. 

" Now we shall probably be well within the mark if we assume 
that for every fatal case of illness there are from four to five 
more cases which end in recovery. This is about the proportion 
in enteric fever, which is a more fatal disease than the average 
of diseases. The result, therefore, on this assumption would be 
that, speaking in round numbers, there were 500,000 fewer cases 
of illness, and 92,000 fewer deaths in England and Wales in 
1881 than would have been the case had the population been 
living under the conditions that existed m 1862-71. It may, 
perhaps, be objected, and not unreasonably, that the year 1881, 
with its extraordinarily low death-rate, was so exceptional, that 
it can hardly be taken as a fair sample by which to measure 
the annual return in life and health from the moneys spent in 



CLIMATIC AND SOCIAL CONDITIONS. 



151 



sanitary improvements. Let us, then, take the entire period of 
ten years that elapsed between the first I'ublic Health Act and 
the close of 1881. Had the death-rate remained during tliat 
period at its mean level in the preceding decade, the total deaths 
from 1872 to 1881 inclusively Avould have been 5,548,116, 
wliereas they were actually no more than 5,155,367. Thus no 
less than 392,7-19 persons who, under the old nujime, would have 
died, were, as a matter of fact, still living at the close of 1881. 
(The mean birth-rates in the two decades 1862-71 and 1872-81 
were almost exactly the same, so that no correction need be made 
in this case.) Add to these saved lives the avoidance of at least 
four times as many attacks of non-fatal illness, and we have the 
total profits as yet received from our sanitary expenditure. More- 
over, it is important to note that these profits were not equally 
spread over the ten years, but that there was a manifest tendency 
to' ])rogressive increase throughout the period. This is what 
might be anticipated ; for the full etiect of sanitary improvements 
requires time for development." The results just described, and 
their continuance and extension in more recent years, may be 
summarized as follows : — 







Mean Annual 




Period of Years. 


Death-rate per 
iOOO living. 




Ten Years, 1862-71 


22-6 


Public Health Act, 1872— 








Four Years, 1872-75 


21-8 


Public Health Act, 1875— 








Five Years, 1876-80 


20-79 




„ 1881-85 


19-30 




,, 1886-90 


18 89 




,, 1891-95 


18-74 




Year 1896 


17-10 




,, 1897 


17-40 



The improvement shown al)ove would have been even more 
striking but for the return of epidemic influenza, after an almost 
complete absence between 1858 and the end of 1889. Since 
December, 1889, this disease has caused a very large number 
of deaths, nor can it be said at present to be within tlie scope of 
active preventive measures. The extent of the decline in the 
death-rate at ditierent ages and in the two sexes will be discussed 
later (p. 315). 



152 VITAL STATISTICS. 

Some alloAvance must be made for the more favourable age- 
constitution of the population in recent years, caused by the 
decline in the birth-rate from its highest point, 36-3, in 1876, to 
29-7 in 1896. Comparing the mean populations for the decennia 
1871-80 and 1881-90, it is found that the numbers of males and 
females living between the ages of 10 and 45 years Avere relatively 
greater in the later than in the earlier decennium. Thus the 
crude death-rate for 1871-80 was 21-27; that for 1881-90 was 
19-08. Corrected for age-constitution, the former becomes 20-84, 
which should be compared with 19-08. {Sup'pleinent to Fifty-fifth 
Report of the Registrar-General, part i. p. viii.) It need hardly 
be said that a continuance of this declining birth-rate will 
eventually cause an age-distribution of population unfavourable 
to a low general death-rate. (See. p. 96.) 

The same lesson as to saving of life is taught by the experience 
of the so-called Healthy Districts. In 1859 Farr published a 
Life-Tahle of the Sixti/-three Healthiest English Districts. These 
were the districts which in 1841-50 had a crude death-rate below 
17-5 per 1000. In 1841-50, less than 6 per cent, of the total 
population lived in districts which, " for the sake of convenience, 
were called healthy districts," and Avhich had a crude death-rate 
below 17-5 per 1000 In 1881-90, on the other hand, 25 per 
cent, of the population lived in districts with a crude death-rate 
below 17-0 per 1000, and 4| per cent, in districts with a crude 
death-rate not exceeding 15>0 per 1000. When allowances were 
made for differences of age and sex-constitution in the several 
districts, it was found that 263 districts, with a mean aggregate 
23opulation of 4,606,503 persons, or about one-sixth of the whole 
population, had death-rates below 15 per 1000 in 1881-90. 
{Sup2)lem.ent to Fifty-fiftli Report of the Registrar-General, part ii. 
p. ciii.) The new healthy district life-table given by Dr. Tatham 
is thus based on the experience of one-sixth of the population of 
the country. 



CHAl'TEi: X\L 



DENSITY OF POPULATION AND MOPvTALITY. 



DR. FARE first called attention to the inHuence exerted by 
density of jjopulation on mortality in the Fifth Rejtort of 
fhe llciiUfrar-General (1843), and since that time statistics hearing 
on the question have regularly apjjcarcd in the Registrar-General's 
reports. 

Method of Calculating Degree of Aggregation of Population. 

Two methods are commonly adopted. (1) The number of persons 
living to each square mile of area is stated. (2) The average 
luimber of acres occui^ied Ijy each person in the population is 
stated. 

The following table gives au examjile of both these methods : — 



England and Wales — Density and Mortality 






IS 51-60. 


1^^01-70. 


1S71-S0. 


lSSl-!)0. 


Death-rate per 1000 
Persons to a Square Mile 
Acres to a Person ( mean density) 


22-2 
325 
1-96 


22-5 
365 
1-74 


21 '4 
416 
1-53 


19-1 
470 
1-35 



If Area --= A, and population = p. 

P 

Then ^ = D = mean population on each unit of area, 

While p - the mean area to each person. 

The unit of space in the first method is taken to Ije a mile ; in 
the second an acre. 

Apparent densities of i)opulation do not always correspond 
with real densities, because the jjopulation in one of the towns 
to be compared may be lodged on only a portion of its area, the 

153 



154 VITAL STATISTICS. 

remaining area being occupied by a lake, common, park, etc. 
The usual plan adopted is to include these (thus diminishing the 
apparent density of population) if they are within the borders of 
the sanitary district. 

Relation between Density and Mortality. Dr. Farr found 
that the mortality increases with the density of the population, 
but not in direct proportion to their densities, but as their 6th 
root. 

Thus, if d and d' = density of population in two places, 
and ?yi and «i' = mortality ,, „ „ 

then — =: / — 

and m' '. m \ '. Xjd' '• Vd 

In his report for 1843, Dr. Farr gives as examples seven 
groups of districts the death-rate of which, calculated from 
their densities, approximated very closeI;y to the observed death- 
rates. Thus — 



Death-rates — 






Calculated : 


18-90— 19-16 -20-87- 


-25 -92—28 -08—37 -70—38 -74. 


Observed : 


16-75 — 19-16— 21-88- 


-24 -90—28 -08—32 -49—38 -62. 



The formula Avas subsequently modified by Dr. Farr {Stqjple- 
ment to Tliirtyjiftli Annual Report, p. clviii.), 0-11998 being 
substituted for \- in the above formula; or, more exactly — 

AfxO-1199S 
''^'\-d) 

Thus, in 1861-70, in the -345 districts which had a mortality 
of 19-2, the density Avas 186 persons to a square mile; in the 
9 districts with a density of 4499, Avhat Avas the mortality? 
It Avas happily not expressed by the proportion of the tAvo 
densities; i.e., 186 : 4499 :: 19-2 : ,/; ; but by this proportion 
nearly — 

(186)0-12 . (4499)0-12 • • 19-2 ; .x. = 28-l, 

i.e., approximately as the 8th root of the density of the respective 
populations. 

This formula only gives slightly different results from the 
preceding one. So closely Avas the ratio found to be folloAved 



DENSITY OF POPULATION. 



155 



in places whose sewage and water supply and other sanitary 
conditions were fairly the same, and which apparently (littered 
only in density of population, that Dr. Farr went so far as to 
propose that in any sanitary inquiry the influence of density 
should first he discovered by means of the al)ove formula, and 
that the ett"ect of other influences above or below this should then 
be investigated. As he remarked, " the formula thus eliminates 
the element of density from the analysis of the causes of 
insalubrity." 

If a constant relationship existed between the death-rate and 
density of population, an increased mortality might be expected 
Avith the course of events shoAvn in the following table : — 

England and Wales : Density of PoruLATioN. 



Date of Census. 


Persons per 
s(iuare mile. 


Acres per 
person. 


Proximity 
in yards. 


ISOl . 


153 


4-20 


153 


1811 . 


174 


3-67 


143 


1S21 . 


206 


3-11 


132 


1831 . 


238 


2 -69 


123 


1841 . 


273 


2-34 


114 


1851 . 


307 


2 08 


108 


1861 . 


344 


1-86 


102 


1871 . 


390 


1-64 


96 


1881 . 


445 


1-44 


90 


1891 . 


497 


1-29 


85 



But the table on p. 151 shows that the death-rate has steadily 
declined with increasing density of population. It is evident, 
therefore, that either the relationship between density of poi^ula- 
tion and niortality is accidental rather than essential, or that 
important countervailing influences are at work. 

Urban and Rural Mortality. There still remains a higher 
death-rate in urban than in rural districts, though the difference 
between the two is becoming gradually less. BetAveen 1851-60 
and 1896 the urban death-rate has declined 27 per cent, (from 
22-2 to 17-1 per 1000), and the rural death-rate 23 per cent, (from 
19 "9 to 15 '3 per 1000). This does not, however, represent the 
exact facts, as only crude death-rates have been used in the 
comparison. In the Supplement to the Fifty-fiftli Repiort of the 



156 



VITAL STATISTICS. 



Registrar-General, p. xlvii., is given a valuable table, reproduced 
below, in v^fhicli groups of districts are classified according to 
density of population, and according to death-rates corrected for 
variations in age-constitution. 

In the following table the above facts are given in the first 
three columns, and in the fourth column are given death-rates, 
which I have calculated on the assumption that Farr's law holds 
good : — 



Density 


Mean crude 
Deatli-rate. 


Mean 


Death-rate 


(Persons to a 


corrected 


according to 


square mile). 


Deatli-rate. 


Farr's Formula. 


(1) 


(2) 


(3) 


(4) 


138 


14 


75 


12-70 


16-36 


149 


15 


73 - 


13-45 


16-52 


187 


16 


30 


14-48 


16 99 


214 


16 


66 


15-41 


17-28 


307 


16 


92 


16 47 


18-08 


435 


17 


59 


17-35 


18-89 


662 


18 


46 


18-55 


19-90 


1281 


]8 


59 


19-39 


21-62 


1803 


19 


53 


20-43 


22-56 


2437 


20 


13 


21-47 


23-43 


3299 


20 


90 


22-50 


24-33 


5329 


21 


96 


23-41 


25-84 


4295 


22 


71 


24-51 


25-15 


5722 


24 


47 


26-22 


26-07 


19584 


30-70 


33-00 


30-40 



The above table deals Avith 632 districts, having a population of 
27,488,482, with a mean deatli-rate of 19-08, and a density of 
471 persons to a square mile. The method of obtaining the 
calculated death-rates in column 4 can be seen from an example : 
the death-rate for all the districts being 19-08, and their mean 
density 471 persons per square mile, Avhat will be the death-rate 
when the density is 19,584 persons per square mile? 

m^ ^ y 19, 584 

19-08 V 471 

1 1 lonQ log. 19,584 -log. 471 
log. w-^-log. 19-08 = —^ ^ ^ 

8 

.•.^1 = 30-40. 



DENSITY OF POPULATIOK. 157 

It will be aeen that crude death-rates overstate the mortality of 
healthy districts, and understate that of unhealthy districts. The 
<leath-rute calculated from the density of population and the 
average death-rate of all the districts by Farr's formula, gives 
too high a death-rate in all the districts except those presenting 
tlie maximum density. It is chietly after the density has reached 
a certain degree of intensity that it begins to exert an appreciable 
effect. As Dr. Ogle says: "This might have been anticipated. 
For though in crowded communities it may be a matter of vital 
importance whether there are 500, or 1000, or 2000, or more 
persons living on a square mile, yet it can scarcely make any 
difference, so far as health goes, whether in rural districts there be 
two acres or three acres on an average to each inhabitant. The 
difierences in the death-rates in these sparse populations are 
determined liy other conditions than aggregation." 

Causes of High Mortality with Increased Density. The 
higher death-rates, which are usually associated with increased 
density of po[)ulation, are not the direct results of the latter. The 
crowding of persons together doubtless leads to the risks of 
fouling of air and water and soil, and to the increased propagation 
of infectious diseases, and thus directly affects the mortalit}'. 
l>ut more important than these are the indirect consequences of 
dense aggregation of population, such as increase of poverty, filth, 
crime, drunkenness, and other vices, and perhaps more than all, 
the less healthy character of urban industries. (See p. 181.) 

(1) Of the direct influences connected with close aggregation 
of })opu]ation, filth roiuUtions of air and water and soil are the 
most important. If the source of water supply is pure and the 
drainage is good, densely populated towns may be, and are, 
commonly better off in these matters than rural districts. But 
atmospheric impurities, especially in the form of decomposing 
organic matter, are doul)tless more rife in town than in country ; 
and Dr. Farr rightly lays special stress on these. Even in towns, 
the amount of such impurities varies greatly in houses of diti'erenfe 
sizes, and such difierences throw a flood of light on the facts 
given on p. 162 regarding the higher mortality in one and two- 
roomed houses. The following table, given in a paper which 
appeared in the Philosophical Transactions for 1887, by Professor 
Carnelly and Drs. Haldane and Anderson, as the result of 
elaborate observations made at Dundee, shows very strikingly 
the differences in houses of varying size. Taking the average 
amount (in excess of outside air) of carbonic acid, organic matter, 



158 



VITAL STATISTICS. 



and micro-organisms respectively in the atmosphere of houses of 
four or more rooms as unity, then in one and tworroomed houses 
the relative amount was as folloAVs : — 





Houses of 
Four Rooms 
and upwards 


Two-room 
Houses. 


One-room 
Houses. 


Cubic Space per person . 
Carbonic Acid 
Oi-ganic Matter 
Micro-Organisms, total . 
Bacteria • • • . 
Moulds 


1 


0-13 

15 

1-6 

5-1 

3-1 

5-5 


0-11 

2-0 

4-4 

6-7 

6-9 

3-0 



(2) The more rapid spread of infectious diseases is shown by 
the higher mortality from the chief infectious diseases in large 
towns, their more rapid spread being partly due to the more 
frequent opportunities of personal contact, and partly, also, to 
the fact that a fouled state of the atmosphere and soil facilitates 
the propagation of infection. 

(3) Other diseases, as phthisis, are more common in urban than 
in rural districts. The close connection between phthisis and a 
foul atmosphere is well established. Dr. Anderson's researches 
in Dundee, and Dr. Russell's in Glasgow, both show that the 
mortality from phthisis in these towns is highest among the 
inmates of three-room houses. The former suggests that the high 
infantile mortality from other forms of tubercular disease returned 
as nervous diseases, atrophy, wasting, etc., prevents the growth of 
young adults (who are most prone to tubercle of the lungs) in the 
houses with less than two rooms. It may be, also, that in the 
one and two-roomed tenements, the children leave home earlier 
than the children living in larger houses. 

(4) Poverty of the inhabitants of densely populated districts, 
implying as it does inadequate food and deficient clothing and 
shelter, has a great effect in swelling their mortality. Dr. 
Drysdale quoted, in a jDaper read at the meeting of the British 
Medical Association in 1887, the loAver mean age at death of the 
industrial classes as evidence that indigence causes a high mortality. 
The fallacy of this test is exposed on p. 294. A similar objection 
applies to Dr. Drysdale's argument, based on the statement that 
among the rich in France, 65 out of every 1000 deaths are due to 



DENSITY OF POPULATION. 159 

tubercular diseases, and 250 per 1000 deaths among the poor. 
The real question is, What are the relative deaths from tubercular 
diseases among equal numbers living at corresponding age- 
groups 1 

(5) Other evil social conditions commonly accompany poverty. 
Cities are commonly the liotbeds of vice and misery, of crime and 
drunkenness, as well as of fdth and "want. The Select Committee 
on Intemperance (4th Report, 1<S78) say: "On the whole, in the 
towns where the drunkenness is greatest, the population is most 
ilense." The density of population ami the drunkenness each of 
them probably stands in the place of both cause and effect. 

Accidents are more common and more fatal in cities than in the 
country. The evil influences of lieredity should also be mentioned, 
physical degeneration occurring among those who, generation after 
generation, are exposed to an unwholesome environment. 

(6) The influence of occupatiori and of homes involving ex- 
posure to poisonous effluvia and other poisonous agencies, will be 
considered in the next chapter. 

The True Test of Density of Population. In a paper on 
" Tlie Vital Statistics of Peabody Buildings " (Royal Statistical 
Society, February, 1891), I showed the inapplicability of Fari-'s 
formula to such Inuldings in which the maximum density of 
population occurs, but which are under generally favoiirable con- 
ditions of life, notwithstanding this fact. Thus during the year 
1889 the number of persons to an acre in London was 58, in the 
Peabody Buildings 751. What ought to be the death-rate in the 
Peabody Buildings, that of London being 17*4 per 1000? 

, ,^ , /75P 

Consequently vi = 24*21. 

But the actual death-rate of the Peabody l)uildings was 1G49 
I)er 1000. Hence the actual death-rate was 7"72, or 31 per cent., 
lower than the death-rate, calculated on the assumption that 
mortality varies with densit}' of po])ulatiou according to the above 
linally modifled formula of Farr. 

I further pointed out that an essential element in testing the 
tiue density of population is a statement of the numher of persons 
tinmi in each occupied room. (See also p. 135.) It is probable that 
tliis test, combined with a determination of the population on a 



160 VITAL STATISTICS. 

given area, would give the most trustwoTthy estimate of density. 
The two together would determine the probabilities of the inci- 
dence of the diseases connected with overcrowding, and of the 
rapid spread of infectious diseases. 

The census returns give information as to the number of houses 
in each district; and in the 1891 census for the first time infor- 
mation was required as to all tenements with less than five rooms. 
The definition of " house " in the census instructions' was all ilie 
space witMn ilie exiernal and party icalls of a huildinriy however 
many families living in separate tenements or apartments might 
be comprised Avithin it. A "tenement" Avas defined as any house 
or pa7't of a house separately occupied either hy the oivner or by a 
tenant. Xo definition of "room" was given, and it is possible, 
therefore, that in small tenements error might arise by the 
inclusion of lobbies, closets, etc. The information obtained must, 
therefore, be regarded as only furnishing rough indications. 

At the census of 1891 there were in England and Wales 
5,451,497 inhabited houses, and an average number of 5"32 
persons to each inhabited house, against 5-38 in 1881, and 5-33 
in 1871. The population varies greatly in difterent parts of the 
country, and there cannot be considered to be any direct rela- 
tionship between the average number of persons per house and 
overcrowding, as the size of houses and the proportion of tenement 
dwellings varies greatly in different communities. The proportion 
of persons per house does not, hoAvever, appear to vary greatly in 
individual towns, as shown by the following examples. 

Population per Inhabited House. 





ISSl. 


1S91. 




1881. 


1891. 


Birmingham 


. 5-12 


5-01 


London . 


. 7-84 


7-72 


Bradford . 


. 4-88 


4'72 


Manchester 


. 5-09 


5-04 


Biit^hton . 


. 6-20 


5-93 


Norwich . 


. 4-45 


4-53 


Unh 


. 4-77 


4-71 


Portsmouth 


. 5-64 


5-43 


Leicester . 


. 4-93 


4-89 


Sunderland 


. 7-24 


7-00 



A tenement may, in the terms of the preceding definition, 
coincide with an entire house ; thus in England and Wales, in 
1891, there Avere T12 tenements, or distinct occupancies, to each 
inhabited house. 

The following table, summarized from a table on p. 4, vol. iv. 
of the Census Report, 1891, gives the main facts as to tenements 
at the time of the last census : 



DENSITY OF POPULATION. 



161 



Teneiiieiits with 


Percentage of 
English Popu- 
lation in each 
class of 
Tenement. 


Averagf! 
Occupants 
per Room. 


Overcrowding. 


Percentage of total Popula- 
tion living in one to four- 
roonierl Tenements, with 
more than two Occupants 
per Room. 


1 room . 

2 rooms . 

3 ,, . 

4 „ . 

5 or more rooms 


(1) 

2-2 

8-3 

11-1 

23-5 

54-9 


(•2) 
2-23 
1-73 
1-42 
1-16 


(3) 
1 23 
3-88 
3-28 
2-84 


100-0 


— 


11-23 



It thus appears that 54-9 per cent., or more than half, of the 
population lived in tenements of more than four rooms ; that 
only 2-2 per cent, lived in single-roomed tenements, 8 3 per cent, 
in two-roomed tenements, and so on. Column 2 shows that the 
fewer the rooms in a tenement the larger the proportion of occu- 
pants per room. In the census report it is proposed to take as a 
standard of overcrowding, tenements which have more than two 
occupants per room. This would exclude all single-roomed tene- 
ments with not more than two inhabitants, all two -roomed 
tenements with not more than four inhabitants, and so on. 
When this is done, it will be seen that 11.23 per cent, of the 
total population occupy overcrowded tenements, the greatest pro- 
portion of these being in two-roomed tenements. 

The preceding facts can be studied in detail for each sanitary 
district in England and Wales in vol. ii. of the Census Report 
(Table 6 in each divisional part). 

Overcrowding in Rural and Urban Districts. 



Tenements with 




1 


Overcrowding. 


tion in each class of 
Tenement. 


Percentage of total Population living in 

one to four-roomed Tenements with more 

than two Occupants per Room 


1 room . 

2 rooms . 

3 „ . . 

4 „ . . 

5 or more rooms 


Urban 
Districts. 


Rural 
Districts. 


Urban Districts. 


Rural Districts. 


2-89 

9-38 

11-54 

22-42 

53-77 


44 

5-65 

1006 

26-26 

57-59 


1-61 

4-42 
3-46 

2-82 


0-25 

2-48 
2-83 
2 90 


100-00 100-00 


12-31 8-46 



162 



VITAL STATISTICS. 



As might have been anticipated, in view of the higher rentals 
in towns, the preceding table shows a higher proportion of one 
and two-roomed tenements and of overcrowding, as defined 
above, in urban districts. When studied in detail, the differences 
between great towns in respect of proportion of population living 
in an overcrowded condition are very striking. (See p. 23, vol. iv., 
Census Rejport.) 

Effects of Higher Degrees of Density on Mortality. Dr. J. 

B. Russell, in an address to the Glasgow Philosophical Society 
(N'ovember, 1888), brought out very strikingly the connection 
between size of the average house and the general death-rate. 
Aberdeen, which has 13-6 per cent, of its population living in one 
room, had the lowest death-rate of eight great Scotch towns, the 
death-rate rising pari j^cissu with the diminution in size of the 
average house, until we come to Glasgow with 24"7 per cent, of 
its population living in one room, and the highest death-rate. In 
comparing the twenty-four districts into which Glasgow is divided, 
the same general relation was demonstrated. The population of 
Glasgow in 1885 was 543,295, the number of deaths 13,439. 
The distribution of population and deaths in the inhabited houses 
accordinsj to their size was as follows : — 



Size of House. 


Population. 


Deaths. 


Percentage of 


Population. 


Deaths. 


One room 

Two rooms 

Three ,, . . . 

Four „ ... 

Five rooms and upwards . 

Institutions 

Untraced 

Whole city 


134,728 

243,691 

86,956 

32,742 

38,647 

6,531 


3636 
6325 
1747 
581 
434 
427 
289 


24-7 

44-7 

16-0 

6-1 

7-1 

1-4 


27-0 
47-0 
13-0 
4-3 
3-3 
3-2 
2'2 


543,295 


13,439 


100-0 


100-0 



It will be seen that in both one and two-room houses the 
deaths were 2-3 per cent, above the due proportion, while in the 
houses above this size they were all below the due proportion 
in varying degree. The difference betAveen the distribution of 
population and deaths may be seen at a glance from Dr. Russell's 
diagram. 



DENSITY OF POPULATION. 



163 





Populatiou. 



Fig. 20. 



Deaths. 



The one and two-room houses mentioned above are commonly 
"made-down houses," i.e., parts of houses of larger size, which 
are now let separately. In some cases single rooms are divided 
by wood partitions, and let to two separate families. 

If the death-rates in these various classes of the population be 
compared, the deaths in institutions and the unallocated deaths 
being placed, as in the diagram, along with the deaths contributed 
by one and two-room houses — it will be found that among those 
living in one and two-room houses, the death-rate is 27 "74 per 
1000; among those living in houses of three and four rooms, 
19-45; and among those living in houses of five rooms and 
upwards, only 11 "23. 

Next as to the incvJence of certain classes of disease upon these 
sections of the population, Dr. Russell selected zymotic diseases ; 
diseases of the lungs, including consumption ; diseases special to 
children under five years of age (as convulsions and other diseases 
of the nervous system, atrophy or wasting, and premature birth) ; 
deaths of children from accident and syphilitic disease, "a small 
class, but one pregnant with meaning." In the following table 
the rates per 100,000 inhabitants from each of these are shown : — 





0ns and 

Two-Room 

Houses. 


Three and 

Four-Room 

Houses. 


Five Rooms 
and upwards. 


Zymotic Diseases .... 
Acute Diseases of the Lungs (inchicl- 

ing Consumption) 
Nervous Diseases and Diseases of 

Nutrition in children . 
Accidents and Syphilis in children 
Miscellaneous Unclassified Diseases . 

All Causes 


478 

985 

480 

32 

799 


246 

689 

235 

11 

764 


114 

328 

91 

590 


2774 


1945 


1123 



164 



VITAL STATISTICS. 



The same results are exhibited in the following diagram, 
in which, the three columns being drawn on the same scale, 
the comparative general death-rate in the three grades of houses, 
as Avell as the comparative prevalence of these classes of disease, 
can be seen by the height of the columns and their different 
positions. 

It will be observed that in the preceding example no correction 
is made for varying age-constitution of the population in each 
class of dwellings. An allowance of uncertain amount must be 
made for this factor. 

It would be a mistake to suppose that the ratio between 
density and mortality represents an inexorable law incapable of 
mitigation. That this is not so, is shown by the following 



(1) 




(3) 


: "V^i 


(4) 


^ ^' 




k 




•V.-S" 




Fig. 21. 

(1) Zymotic Diseases. (2) Nervous and other Diseases special to Cliildren. 

(3) Accidents and Syphilis in Children. (4) Diseases of the Lungs. 

(5) Miscellaneous. 



DENSITY OF POPULATION. 165 

example, derived from the paper by tlie author ah'eady quoted 
(pp. 135 and 159). 

Peabody Block Dwellings. These dwellings in December, 
1890, had an enumerated population of 20,374. These occupied 
5071 tenements containing 11,275 rooms. The average number 
of persons per tenement was 4 "03, the average number per room 
was 1"81. These were occupied by families, the average Aveekly 
earnings of which were less than 24s. The age-distribution of 
the i)opulation of these buildings was such that the factor of 
correction was 1*0391 as compared Avith 1*0615 for London as a 
whole. The general results of my investigation into the vital 
statistics of the Peabody Buildings Avere summarized as follows : — 

(1) The death-rate of the Peabody Buildings averaged about 
2 per 1000 lower than that of London during the twelve years 
ending with 1885. During the four subsequent years the death- 
rate of the Peabody Buildings remained about stationary, while 
tliat of London has shown a further decline ; thus making the 
metropolitan death-rate approximate more closely that of the 
Peabody Buildings. 

(2) The death-rate at different groups of ages was lower in the 
Pealiody Buildings than for the Avhole of London with the excep- 
tion of the ages 0-5 and 15-25. 

(3) The infantile mortality was much lower in the Peabody 
Buildings than for all London. During the nine years 1882-90 
it averaged in London 151 '9, in the Peabody Buildings 139*2 
per 1000 births. 

(4) The death-rate from diarrhoea was slightly lower than, and 
from enteric fever only half that of the whole metropolis. 

(5) On the other hand, the diseases more immediately due to 
direct infection (scarlet fever, diphtheria, and still more Avhooping- 
cough and measles) Avere more fatal, and therefore probalily more 
prevalent. The two last-named diseases are not admitted into 
the hospitals of the Metropolitan Asylums Board. 

(6) The death-rate from phthisis and other tubercular diseases 
is slightly higher in the Peabody Buildings than for all London. 

(7) Farr's formula as to the increased mortality Avith increased 
density of population has no application to the Peabody Buildings. 

(8) The true density that should be considered is the number 
of persons to each room, not the number of persons on a given 
acre. (See also pp. 135 and 159). 



166 



VITAL STATISTICS. 



Back-to-Back Houses are still common in several toAvns in tlie 
North of England, and on general grounds it might be expected 
that the deficient light and ventilation, and the imperfect sanitary 
arrangements necessarily associated Avith this style of dwelling, 
must have an appreciable effect on the health and vitality of their 
inhabitants. Discrepant statistics have, however, been published, 
and they are given here as illustrating the difficulty of avoiding 
errors aiad fallacies. 

ISlv. Gordon Smith and Dr. Barry, in their report to the Local 
Government Board on back-to-back houses, gave the foUoAving 
death-rates from figures furnished by Dr. Tatliam. 

The Greeiigates and Regent Road registration sub-districts of 
Salford were each divided into three groups, as shown in the 
folloAving table, Avhich Avill enable the relative mortality of each 
from various special causes to be seen at a glance : — 





Popu- 
lation. 


Deatli-rate per 1000 Uving from 


All 
Causes. 


Pulmonary 
Diseases, 
excluding 
Phthisis. 


1 


Seven 

Chief 

Zymotic 

Diseases. 


Diar- 
rhoea. 


Greengates Sub-District. 

Group I. — No back-to-back 
houses .... 

Group II. — Average propor- 
tion of 23 per ceut. of 
back-to-back houses . 

Group III. — A Average propor- 
tion of 56 per ceut. of 
back-to-back houses . 

Eegent Road SiLh-District. 

Group I. — No back-to-back 
houses .... 

Group II. — Average propor- 
tion of 18 per cent, of 
back-to-back houses . 

Group III. — Average propor- 
tion of 50 per cent, of 
back-to-back houses . 


8,713 
11,749 
11,405 

54,264 

8,773 
4,380 


27-5 
29-2 
30-5 

26-1 
29-1 
37-3 


6-6 

7-8 
7-9 

57 
7-5 
8-6 


2-8 
3-3 
3-6 

2-7 
2-7 
4-5 


4-5 
4-8 
6-2 

4-9 
4-9 
7-6 


1-42 
1-55 
2-12 

1-54 
1-85 
2-83 



It Avill be seen that the mortality from all causes, from pul- 
monary diseases, from phthisis, and from the seven chief zymotic 
diseases taken together, as Avell as from diarrhoea alone, increase 
pari passu AA'ith the proportion of back-to-back houses. 



DENSITY OF POPULATION. 167 

Tlio (lifTiculty here, as in all siiuilur inquiries, consists in ensuring 
that the populations thus contrasted have a similar age and sex- 
constitution, and that apart from the character of the houses the 
other conditions of life are equal in the contrasted groups. 

Dr. J. II. Bell {Public Health, vol. iv. p. 143, 1892) advances 
the opinion that back-to-hack houses are not essentially insanitary, 
and gives a table, of which the following is a summary : — 





No. 1. 


No. 2. 


No. 3. 


Total No. of liouses 


669 


757 


703 


Total No. of persons 


2808 


3428 


3583 


Average No. of square yards to each 








house ..... 


116 


122 


134 


Weekly rental, including rates 


4/6 to QjQ 


4/6 to 5/6 


5/- to 7/6 


Mean annual death-rate per 1000 for 








1886-90 (No. 2, 1889-90 only) . 


15-8 


16-6 


17-0 



The mean annual death-rate of the entire borough of Bradford, 
in which the above dwellings were situate, was 21 "3 per 1000 in 
1886-90. 

No. 1 consisted of continuous back-to-back houses. 

No. 2 of back-to-back houses in blocks of four. 

No. 3 of through houses. 

The defects of tliii above statistics were clearly pointed out by 
Dr. Arnold Evans, the Medical Officer of Health of Bradford. 
(Ptihlic Health, vol. iv. p. 145.) Thus no particular diseases are 
enumerated, only total death-rates. Further, Dr. Bell "had 
picked out a few streets here and there containing through houses, 
and compared their death-rates with those of whole groups of back- 
to-back houses." Again, many of the through houses selected 
were old and defective, and situate in narrower streets and at a 
lower level than the back-to-back houses, and so on. 

The statistics least open to objection on this subject are those 
compiled by Dr. Herbert Jones (Public Health, vol. v. p. 347, 
1893), in which back-to-back liouses in Shipley are contrasted 
with houses similar in other respects, except in being through- 
houses, in the neighbouring compact village of Saltaire. The 
soil, water-supply, aspect, sanitary arrangements, and the building 
material of the houses in the two groups are identical. The 
statistics are taken for the six years 1887-92. The density of 
the population and the ages of the houses were approximately 
equal in the tAvo groups; so also was the relative amount of 
pauperism. 



168 



VITAL STATISTICS. 



Saltaire "Through" Houses compared with some 
Back-to-Back Houses. 











f*-< 




Death-rates per 1000. 




o 


p. . 


p< 


o ^ 


■S 

IS 






"" d 








o 


a S 
o o 


2£ 


fin 






1 


«-2 


1 

1-08 


C3 
& 
JS 

CS 
5 

•22 


" Throngli " . 


4,218 


4-9 


197 


•42 


3/6 to 51- 


15-6 2-7 


3-6 


Back -to -back . 


4,] 55 


4-8 


222 


•47 


2/6 to 7/- 


21^1 3-4 


5^1 


1-7 


■40 


Shipley District 


16,000 


— 


— 


— 


— 


16-2 2^3 


4-0 


1-7 


•22 


Back-to-back A 


2,200 


47 


160 


•17 


4/- to 7/- 


18-1 2^8 


4 9 


1-3 


•22 


)) 1) ^ 


710 


4-7 


300 


•42 


3/- to 3/6 


28-1 4-6 


7-4 


29 


•84 


)) >> ^ 


1,245 


4-9 


207 


1-04 


2/6 to 4/6 


22-5 41 


5^7 


1-8 


.4 



For the six years 1887-92. 



The table shoAvs excess of zymotic diseases, and still more of 
phthisis and of respiratory diseases in the hack-to hack houses. 
The hack-to-hack houses were divided into three sections : A, with 
streets twenty-five yards wide ; B, with streets ten yards wide ; 
and C, Avitli streets fifteen yards Avide, with the comparative 
results shown in the above table. 



CHArTEPt XVII. 

OCCUPATION AND MORTALITY. 

IN vol. iv. p. 35 et seq. of the Census Keport, 1891, the un- 
satisfactory character of the census data as to occupations of 
the po})uhition is ])ointed out. Tlie instructions contained in 
each "Householder's Schedule" stated that persons "should state 
distinctly, not only the general name of the industry in which 
they are emjjloyed, hut the particular branch of the industry in 
Avhich they are engaged, and also the material in which they 
work, if it be not implied in the name, and if such name be 
common to several industries," and sj^ecial illustrative examples 
were given. But these instructions were largely disregarded, 
the words "spinner" and "miner," for instance, being given 
without mention of the material in which the stated Avork was 
done. It is evident, as pointed out in the Census Eeport, that 
schedules filled up by the householder do not supjdy data which 
are suitable for minute classification, or admit of profitable 
examination in detail. "The most that it is reasonable to expect 
from data so collected, is tliat they shall give the means of draw- 
ing such a i^icture of the occupational distribution of the people 
as shall be fairly true in its main lines, though little value can be 
attached to the detailed features." 

Fresh headings were introduced into the schedules for the 1891 
census, to meet the criticisms that in former enumerations distribu- 
tion had not been kept separate from production, and that masters 
had not been distinguished from their workmen. It is pointed 
out, however, on the first head, that the distinction between 
makers and dealers is not so well marked in actual life as in 
economical science ; a baker or a shoemaker, for instance, may be 
a person who makes bread or shoes, or a person who merely sells 
these. To meet the second objection three new columns Avere 
introduced, headed respectively "employer," "employed," and 

169 



170 VITAL STATISTICS. 

"neither employer nor employed," but the returns made under 
these three heads were " excessively untrustworthy." 

Classification of Occupations. At the 1891 census, occupa- 
tions in combination with ages were abstracted under 349 headings, 
and then arranged in sub-orders, orders, and classes. Six larger 
groups or classes were made, viz. : — 

Professional, 

Domestic, 

Commercial, 

Agricultural, 

Industrial, and 

Unoccupied. 

The lines of demarcation between these are not very definite, 
though the classification is useful. Rules were laid down for the 
guidance of the clerks engaged in tabulating the occupations. 
As it is desirable that a similar method should be adopted by 
medical officers of health in arranging the occupational death 
statistics of their own districts, these rules are given here : — 

"Apprentices, journeymen, assistants, and labourers were to be 
classed under the occupation to which they were apprenticed, or in 
which they assisted or worked, but messengers, errand boys, porters, 
and watchmen (excepting railway or government), Avere not to be so 
classed, but to go to a special heading provided for them, namely, 
Messenger, Porter, Watchmen (not Kailway or Government). 

" Clerks were not classed under the business in which they worked, 
but under Commercial Clerks. To this, however, bank clerks, in- 
surance clerks, and railway clerks formed exceptions, going respectively 
to Bank Officials and Clerks, Insurance Service, and Railway- Officials 
and Clerks. 

" Persons stated to have retired from business were not classed under 
their former occupations, but inider a special heading 'Retired from 
business.' To this rule, however, officers in the Army or Navy, clergy- 
men, and medical men were exceptions. 

"Patients in lunatic asylums and inmates of workhouses over 60 
years of age were not classed by their previous occupations. But 
paupers under 60, patients in general hospitals, and prisoners were 
classed by their occupations as being possibly only temporarily de- 
barred from them, and the same rule was applied to persons stated to 
be ' out of employ ' from any stated handicraft. 

" When a person was returned with several occupations, the rules 
laid down for selection of the one under which he was to be classed 
Avere, firstly, that a mechanical handicraft or constructive occupation 
should invariably be preferred to a shopkeeping occupation ; secondly. 



OCCUPATION AND MORTALITY. 171 

that, if one of the diverse occupations seemed of more importance 
than the otliers, it should be selected ; and thirdly, that in default of 
such apparent difference, the occupation first mentioned should be 
taken, on the ground that a person would be likely to mention his 
main business first." 

The total number of males, 10 years of age or over, returned 
as engaged in some definite occupation, was 8,883,254, or 88-9 per 
cent, of all the enumerated males of those ages ; while the total 
number of females similarly returned was 4,016,230, or only 35 
per cent, of all persons of that sex over 10 years of age. It is 
obvious, however, that this excludes the most important of female 
occupations, the management of domestic life and the rearing of 
children. 

Methods of Comparison between Occupations. (1) The mean 

ages at death of those engaged in different occupations are con- 
trasted. This often, however, gives erroneous indications. The 
mean age at death is governed by the mean age of the living, and 
it is as much affected by the ages at which people enter and leave 
any given occupation, and by the increase or decrease of employ- 
ment, as by its relative salubrity or insalubrity. In a large printing 
firm known to the writer, all the older employes have been replaced 
by youths from fifteen to twenty-five years of age at lower wages. 
Such a proceeding Avill obviously lower the mean age at death, but 
will by no means demonstrate that this particular printing establish- 
ment is carried on under less healthy conditions than formerly. 

(2) The proportion between the number engaged in and the 
number dying in any given occupation, expressed as a rate per 
1000, is also fallacious. As we have already seen, p. 103, the 
death-rate in the general population varies greatly at different 
groups of ages. The death-rate among those engaged in any one 
trade or profession would similarly vary according to the relative 
number at the different ages engaged in it. In other words, it 
Avould depend on the ages of the living, which would vary in 
every occupation, (a) according as persons enter it early or late in 
life, and (J)) according as the numbers that annually enter it 
increase or decrease. Dr. Farr, in his Fourteenth Report, gives 
the following example of the mistakes Avhich would follow the 
adoption of this method. The death-rate of all farmers over 20 
years of age was 28 per 1000, of all tailors 20 per 1000; but 
when tested by a comparison of the death-rate among men of 
corresponding ages, farmers were much healthier than tailors, as 
seen in the following table : — 



172 VITAL STATISTICS. 

Death-eate per 1000 at six Age-guoups op Farmers and Tailors. 



Age. 


25- 


35- 


45- 


55- 


65- 


75- 


Farmers 
Tailors 


10-15 
11-63 


8-64 
14-15 


11.09 
16-74 


24-90 
28-18 


55.30 

76-47 


148-62 
155-28 



(3) The only trustworthy method is to compare the mortality of 
those engaged in one occupation, and of a given age, Avitli the 
mortality of those engaged in another occupation, and of a corre- 
sponding age. 

Statistics of Occupational Mortality. The successive de- 
cennial supplements issued from the General Eegister Office 
have embodied most valuable information on this subject, and 
the last one, prepared by Dr. Tatham, is the most complete and 
detailed of the series. The figures and facts given in the 
remainder of this chapter are derived almost exclusively from 
this report. 

The three successive decennial supplements of Doctors Farr, 
Ogle, and Tatham, all adopt the period of life between 25 and 65 
years of age as being that in which the influence of occupation is 
most felt. It is to be remembered, however, that the working 
period both begins and ends at an earlier date in life in the 
industrial occupations than in the learned professions. 

We have on p. 171 given an illustration showing the fallacy 
involved in comparing the death-rate of all farmers over 20 
with that of all tailors over 20. The following further example 
is taken from Dr. Tatham's Eeport. (p. viii.) At all ages over 
15, the mortality of all males in 1890-92 was 18-74 per 1000, 
and that of farmers 19-58. But when the numbers living and 
dying at each group of ages are compared, the following result 
is obtained : — 



All males . 
Farmers . 

Mortality of farmers \ 
to that of all males > 
taken as 100. ) 


15- 


20- 


25- 


35- 


45- 


56- 


65 and 
upwards. 


4-14 
1-30 


5-55 
2-40 


7-67 
4-29 


13 01 
7-03 


21-37 
11-20 


39-01 
23-97 


103-56 
87-81 


31 


43 


56 


54 


52 


61 


85 



OCCUPATION AND MORTALITY. 



173 



Tlie paradox of a high general death-rate among farmers along 
with a lower death-rate at each age-group is explained by the 
facts that, wliile there are nearly three-fourths as many farmers 
above 65 years of age (with a mortality of 87'8 per 1000) as 
tliere are at ages between 25 and 35 (with a mortality of 4*3 
per 1000) : among all males the number over 65 (with a death- 
rate of 103 '6 per 1000) is less than one-third of the number 
between 25 and 35 (with a death-rate of 7 '7 per 1000). 

A similar objection holds if the crude death-rate at the entire 
age-period 25-65 is taken; as in different occupations there are 
great variations in age-constitution within these limits. This can 
be met by the calculation of death-rates in a standard popula- 
tion. The standard pojjulation thus taken is the number of men 
aged 25-65 in the whole population, out of whom 1000 deaths 
would occur in a year, the deaths of 1890-92 and the population 
of 1891 being taken as the basis. 

This number was 62,215 men, viz. : — 

22,586 in the age-group 25-35 years 
17,418 „ „ 35-45 „ 

12,885 „ „ 45-55 „ 

8,326 „ „ 55-65 „ 



Aged. 


Standard 
Population. 


Death-rate per 1000 living 
in each Age-group among 


Calculated number of Deaths 
in Standard Population among 


All Males. 


Medical 
Practitioners. 


All Males. 


Medical 
Practitioners. 


25-35 
35-45 

45-55 
55-65 


22,586 

17,418 

12,885 

8,326 


6-69 
14-92 
21-04 
34-16 


7-67 
13-01 
21-37 
39-01 


173 

227 
275 
325 


151 
260 
271 
284 


1000 


966 



The death-rate in each age-group in a given occupation, based 
on the death statistics for 1890-92 and the census enumeration 
of 1891, is applied, as shown in the preceding table, to the 
standard population, and the calculated number of deaths thus 
obtained gives the " comparative mortality figure " for the occupa- 
tion in question. For all males it is 1000, for doctors 966, and 
so on. If the calculated deaths in each of the four age-groups be 



174 VITAL STATISTICS. 

proportionately divided out according to the causes of death in 
that age-group, the comparative mortahty figure for the several 
causes of death is obtained. In Table IV. of the last decennial 
supplement this has been done for each of 100 selected occupa- 
tional headings, and also for grouped and for subsidiary headings. 

Sources of Error in Occupational Statistics. Even Avhen the 
correct methods described in the last paragraph are adopted, there 
are certain sources of possible error in the vital statistics of 
occupation. 

(1) The vagueness with Avhich the occupation may be entered 
in the census or mortality returns has been already mentioned. 
For this reason only vt^ell-defined occupations are taken in the 
decennial supplement of the Registrar-General. 

(2) A still more serious difficulty is pointed out by Dr. Ogle, 
for which there appears to be no remedy, and which must 
always to some extent diminish the value of all calculations 
of the death-rate in different industries. Many trades, as that of 
a blacksmith or miner, require great muscular strength, and must 
be given up by persons who become weakly ; and the latter may 
then raise the mortality of the lighter occupations to which they 
resort. Thus the death-rate of the more laborious occupations 
is unfairly lowered as compared with the death-rate (a) of those 
engaged in lighter occupations, or (6) of those who are returned 
as having no occupation, or (c) of those who have to betake 
themselves to odd jobs, as general labourers, messengers, coster- 
mongers and street-sellers. 

(3) Another flaw in occupational death-rates, when taken as 
tests of relative healthiness, is the fact that those who follow 
the several industries do not start on equal terms as regards 
healthiness. A weakling will not become a navvy, but a shop- 
man or tailor by preference. The occupations demanding great 
muscular strength and activity, to some extent then, consist of 
picked men, stronger at the commencement, and maintained up 
to a certain standard by the fact that weaklings are drafted into 
lighter occupations. 

After making full allowance for the preceding difficulties, the 
death-rates of different occupations still furnish most valuable 
indications of the relative salubrity of different occupations ; and 
while small differences may be accidental, large differences must 
be taken as representing real differences of healthiness in the 
various occupations. 



OCCUPATION AND MORTALITY. 



175 



Mortality in Different Occupations. It is impossible here to 
reproduce the elaborate tables given in Part 11. of the Supplement 
to the Fifty-fifth Annual Report of the Retjistrar-General, p. cxix. 
et seq. We must content ourselves with a statement of the 
comparative mortality figures in some of the chief occupations, 
and refer the reader to the above-mentioned tables for further 
jiarticulars and for the actual death-rate of persons engaged in each 
occupation at eacli ten-yearly age-group. 

A preliminary dilhculty arises in comparing Dr. Tatham's com- 
parative mortality figures for 1890-92 with those of Dr. Ogle 
for 1880-82, based on the fact that the latter were obliged to be 
calculated on the death-rates in the two age-groups 25-45 and 
45-65, applied to a population of 64,641 men, of whom 41,920 
were between 25 and 45, and 22,721 were between 45 and 65 years 
of age ; while, in the former, death-rates for four age-groups were 
available, and the standard population of 61,215 men had a 
slightly different age-constitution from the above. For this 
reason Dr. Tatham has calculated " modified mortality figures " 
by taking the death-rates at ages 25-45 and 45-65 in the chief 
occupations, and applying them to the standard population in 
1891 of 61,215 men, of whom 40,004 were between 25 and 45, 
and 21,211 between 45 and 65 years of age. In the following 
table these three sets of comparative mortality figures are given, 
and in the first column is given the more accurate comparative 
mortality figure for 1890-92, based on four age-groups: — 

Comparative Mortality Figures op Males from 25 to 65 
Years of Age, engaged in different Occupations. 



Occupation. 


Comparative Mortality Figure 


Calculated 

on Four 
Age-groups. 


Calculated on Two Age-groups 
(Modified Mortality Figure). 


1S90-92. 


1S90-92. 


18S0-82. 


1860, '61, '71. 


All Males 

Males in Selected Healthy 

Districts 
Occupied Males 
Unoccupied Males . 


1000 

679 

953 

2215 


1000 

693 

947 

2338 


942 

910 
2065 


960 


Clergyman, Priest,Minister 
Gardener, Nurseryman, 
Seedsman 


533 
553 


547 
568 


524 
564 


605 

642 



Table continued on next page. 



176 



VITAL STATISTICS. 



Occupation. 


Comparative Mortality P'if 


;ure 


Calculated 

on Four 
Age-groups. 


Calculated on Two Age-groups 
(Modified Mortality Figure). 


1890-92. 


1890-92. 


1880-82. 


1860, '61, '71. 


Farmer, Grazier 


563 


.591 


595 


673 


Schoolmaster, Teacher 


604 


571 


677 


893 


Grocer, etc. 


664 


664 


726 


744 


Labourer, etc., in Agricul- 










tural Districts 


666 


681 


660 


— 


Goal-miner( Derby & Notts.) 


727 


693 


691 


— 


Sawyer .... 


768 


789 


802 


798 


Artist, Engraver, Sculptor, 










Arclaitect . . . 


778 


777 


868 


955 


Carpenter, Joiner 


783 


779 


772 


831 


Barrister, Solicitor . 


821 


820 


793 


882 


Fisherman 


845 


843 


752 


786 


Shopkeeper (including 










stationer, chemist, to- 










bacconist, fishmonger. 










fruiterer, grocer, draper. 










ironmonger) 


859 


856 


827 


— 


Medical Practitioner 


966 


957 


1058 


1073 


Tailor . . ' . 


989 


999 


990 


1043 


Wool, "Worsted Manufac- 










ture (W. Riding) . 


996 


986 


971 


— 


Bricklayer, Mason, Builder 


1001 


1002 


913 


1033 


Goal-miner (Lancashire) . 


1069 


1026 


874 


— 


Law Glerk 


1070 


1028 


1084 


1536 


Butcher .... 


1096 


1066 


1103 


1130 


Printer .... 


1096 


1048 


1009 


1144 


Plumber, Painter, Glazier 


1120 


1091 


1132 


1234 


Cotton, Linen Manufac- 










ture (Lancashire) . 


1176 


1122 


1024 


— 


Carman, Carrier 


1284 


1247 


1201 


— 


Slater, Tiler . 


1322 


1305 


888 


1078 


Tool, Scissors, File, Saw, 










Needle-maker 


1412 


1398 


1198 


1169 


Brewer .... 


1427 


1407 


1282 


1552 


Innkeeper, Inn, Hotel-ser- 










vant .... 


1659 


1665 


1525 


1490 


Potter, Earthenware, etc.. 










Manufactvire 


1706 


1639 


1638 


1390 


File-maker 


1810 


1791 


1569 


1548 



The preceding table is to be read as follows. The same number 
of men, aged 25-65 (having equal numbers at the various 
inclusive ages), that would give 1000 deaths among all males, 



OCCUPATION AND MORTALITY. 



177 



would give 533 among tlie clergy, 1810 among file-makers, and 
so on. 



Occupational Mortality Distributed according to Causes. It 

is only possiljle here to summarize some of the chief results. "We 
may first compare occupied and unoccxipied men. The preceding 
table shows the comparative mortality figure of the former to be 
953, of the latter, 2215. Doubtless at the earlier ages, the bulk 
of the unoccupied are those who are physically unfit for employ- 
ment ; later on they become eliminated by the high death-rate 
among them, but their place is partially taken by recruits from 
the ranks of the employed. 

The following table (p. xvi., op. cit.) shows how in each case 
the comparative mortality figure is made up : — 



Cause of Death. Occ^^P'^^l 


Unoccupied 
Males. 


Diseases of Nervous System 

Phthisis 

Diseases of Circulatory System 
Influenza and Diseases of Respiratory 

System (except Bronchitis) . 
Cancer ....... 

Diseases of Urinary System 
Alcoholism and Diseases of Liver 
Diseases of Digestive System (exccjit 

Liver Diseases) 

Accident (including Plumbism) 

Suicide ....... 

Bronchitis ...... 

Rheumatic Fever 

All other causes 


82 
185 
126 

166 
44 
41 
40 

28 
57 
14 
88 
7 
75 


630 

448 
240 

266 
96 
82 
76 

43 
81 
28 
84 
2 
189 


All Causes 953 


2215 



In the table on p. 176, some of the chief occupations are 
ranged in order of their comparative mortality. It is interesting 
to follow out the occupations there enumerated, and discover to the 
comparative immunity from or excess of what particular diseases 
they owe their relative positions. This can be done by means of 
Table IV., op. cit., p. cxlv. et seq., from which the following 
typical examples are taken : — 



178 



VITAL, STATISTICS. 



15 . 



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1014 
1284 
1659 
1706 
1810 


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1. 

% 
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Clergyman, Priest, 
Minister . 

Barrister, Solicitor . 

Medical Practitioner . 

Draper 

Carman, Carrier . 

Innkeeper . 

Potter. 

Pile-maker . 



OCCUPATION AND MORTALITY. 179 

The comparative mortality figure among all occupied males 
(953) from Influenza is 33. As might be expected, the highest 
comparative mortality figures from this disease are among those 
most exposed to infection. Thus medical practitioner (96G) 51, 
innkeeper, London (1685) 61, milk-seller (lOGl) 60. The lowest 
are tin-miners (1409) 12, mechanic (399) 12.* 

Alcoholism will he separately considered. 

Rheumatic Fever is responsible for a comparative mortality 
figui'e among all occupied males of 7, varying from 2 for hatters 
(1109) and brass-workers (1088), 3 for shoemakers (920) and 
locksmiths (925), to 10 for teachers (604:), 11 for clergymen 
(533), 19 for publicans (1642), 25 for mine service (1021), 26 
for hotel servants (1583), and 28 for copper-miners (1230). 

GrOUt causes a comparative mortality of 2 among occupied 
males, varying from for fishermen (845), drapers (1014), hatters 
(1109), bookbinders (1060), and some other occupations, to 7 for 
saddlers (924), 10 for gunsmiths (1228) and plumbers (1120), 
and 16 for innkeepers in agricultural districts (1320).* 

Cancer is responsible for a comparative mortality figure of 
44 among occupied males, varying from 22 among paper manu- 
facturers (904), 26 among Welsh coal-miners (1145), and 36 
among farmers (563), to 60 among barristers (821), 63 among 
commercial travellers (961), 70 among brewers (1721) and 
London innkeepers (1685), 73 among tallow, glue, and soap 
manufacturers (1109), and 156 among chimney-sweeps (1311). 

For Phthisis the comparative mortality figure for occupied 
males is 185, the lowest on the list being clergymen and ministers 
67 (533), railway engine drivers and stokers 76 (810), farmers 
and graziers 79 (563), brick burners 84 (741), coal merchants 95 
(803), and coal-miners 97 (925) ; the mortality figure rising until 
it becomes 325 for dock and wharf labourers (1829), and for 
messengers and porters (1222), 331 for coj^pcr-miners (1230), 
333 for potters (1706), 336 for tool, scissors, file, etc. makers 
(1412), 380 for lead-miners (1310), 443 for costermongers and 
liaAvkers (1652), and 476 for inn and hotel servants (1725). It 
will be noted that three of the occupations in which the lowest 

* In each example the comparative mortality /rowi all causes of those en- 
gaged in a particular occupation is given in brackets for convenience of 
reference. 



180 VITAL STATISTICS. 

mortality from phthisis occurs are concerned in the manipulation 
of coal. 

The comparative mortality figure for Diabetes is 7 for all 
occupied males. It is only 1 for messengers and porters (1222), 
3 for locksmiths and gasfitters (925), and for shipwrights (713); 
but ranges up to 17 for the clergy (533), for artists and architects 
(778), and for brewers (1427), 19 for innkeepers (1642), 22 for 
medical practitioners (966), and 28 for barristers and solicitors (821). 

Diseases of the Nervous System show a comparative mortality 
figure of 82 among occupied males. Among the lowest are 
maltsters 44 (884), rope and cord makers 45 (928), farmers 51 
(563), farm labourers 53 (632) ; among the highest, barristers 
and solicitors 104 (821), railway stokers and dockmen 114, 
medical practitioners 122, law clerks 123, brewers 125, innkeepers 
160, file-makers 212, lead- workers 232. 

Valvular Disease of the Heart causes a mortality figure of 
23 among all occupied males, varying from 9 for maltsters (884), 
10 for law clerks (1070), and 13 for chimney-sweeps, to 27 for 
lawyers, 28 for doctors, 30 for teachers (604), 37 for railway 
stokers (810), 40 for lead-workers (1783), 43 for hairdressers 
(1099) and for potters (1706), 44 for fishermen (845), and 47 
for manufacturing chemists (1392). 

For Aneurism the figure for all occupied males was 6, varying 
from for farmers (563), 1 for stationers, etc. (833), 2 for clergy 
(533), 3 for maltsters (884) and drapers (1014), to 8 for artists 
(778) and musicians (1214), 9 for coachmen (1153), 13 for inn- 
servants (1725), 14 for dock labourers (1829) and gunsmiths 
(1228), 18 for bargemen (1199) and seamen (1352), and 28 
for copper-miners (1230). 

Bronchitis produced a mortality figure of 88 for all occupied 
males. The loAvest from this cause were 11 clergy (533), 12 
doctors (966), 15 farmers (563) ; the highest coal-miners 114 (925), 
general labourers 140 (1221), coalheavers 180 (1528), coster- 
mongers 192 (1652), tool, scissors, etc. makers 202 (1412), glass 
manufacture 222 (1487), manufacturing chemists 249 (1392), 
potters 376 (1706). 

The mortality figure for Pneumonia among occupied males Avas 
105, varying from 43 for teachers (604), 45 for clergy (533), 61 
for artists (778), 93 for doctors (966), to 158 for innkeepers (1642), 



OCCUPATION AND MOKTALITY. 181 

184 for carmen (1284), 197 for hotel servants (1725), 220 for 
dock labourers (1829), 248 for iron and steel manufactures (1301), 
and 249 for coallieavers (1528). 

Diseases of the Liver had a comparative mortality figure of 
27 for all occujiied males, being 18 for the clergy, for railway 
guards and porters, for corn millers and for miners, 13 for farm 
labourers, and ranging up to 55 for lawyers, 59 for brewers, 60 
for doctors, and 201 for publicans. 

Bright's Disease. Comparative mortality figure among all occu- 
pied males 27, hosiers 8, farm labourers 12, farmers 18, clergy 27, 
lawyers 38, brewers 55, doctors 56, innkeepers 62, file-makers 82. 

Plumbism. Comparative mortality figure among aU occupied 
males 1, amounting to 15 among tool, scissors and saw-makers, 7 
among potters, 75 among file-makers, and 211 among lead-workers. 

Accident. Comparative mortality figure among all occupied 
males 5G, teachers 8, clergy 9, grocers 16, drapers 19, railway 
guards and porters 137, coal-miners 141, coallieavers 144, seamen 
202, bargemen 223. 

Suicide. Comparative mortality figure, all occupied males 14, 
tanners and railway drivers and stokers 3, clergy and bargemen 7, 
corn millers 8, lawyers 22, chemists 31, innkeepers 32, doctors 37. 

We may summarize, in conclusion, some of the most important 
facts bearing on the influence of foul air, of dust, lead-poisoning, 
and alcoholic excess, on the health of those exposed to their 
effects. 

Effects of breathing Foul Air. The following table {Suijplement 
to the Fifty-Jiftli Annual Report of the Registrar-General, part ii. 
p. xcix.) refers to the statistics of 1890-92, and gives for certain 
selected occujmtions the evidence showing the damage done by 
impure but not necessarily dust-laden air, in the course of these 
occupations. 

" For each of these occuiDations the figures indicating the 
mortality from phthisis, and from diseases of the respiratory and 
circulatory systems are separately shown : and in the third column 
the figures representing the mortality from phthisis and respiratory 
diseases together are compared with the figure for agriculturists, 
the latter being taken as 100. The occupations in the list have 
been arranged in the ascending order of their mortalities from 
phthisis and respiratory diseases combined." 



182 



VITAL STATISTICS. 









Diseases 


Diseases 




Phthisis and 




of 


of 




Diseases of 


Phthisis. 


Respira- 


Circula- 




Respiratory System. 




tory 


tory 


Oocupation. 






System. 


System. 


Mortality 
Figure. 


Ratio. 


Mortality Figure. 


Agriculturist 


221 


100 


106 


115 


83 


Engraver — Artist . 


279 


126 


146 


133 


96 


Shopkeeper (Class) 




350 


158 


172 


178 


117 


Commercial Clerk 




390 


176 


218 


172 


115 


Butcher . 




404 


183 


195 


209 


157 


Saddler . 




417 


189 


248 


169 


133 


Watchmaker . 




427 


193 


234 


193 


94 


Shoemaker 




437 


198 


256 


181 


121 


Draper . 




441 


200 


260 


181 


135 


Tobacconist, To 


jacco 












Manufacturer 




461 


209 


280 


181 


109 


Tailor . 




466 


211 


271 


195 


121 


Hairdresser 




489 


221 


276 


213 


179 


Hatter . 




511 


231 


301 


210 


141 


Musician 




522 


236 


322 


200 


191 


Printer . 




540 


244 


326 


214 


133 


Bookbinder 




543 


246 


325 


218 


115 



Contrary to the experience of two-thirds of the occupied male 
population of England and Wales, phthisis is more fatal than are 
other diseases of the respiratory system in thirteen out of fifteen 
of the groups of workers in the preceding table. 



Effects of breathing Dust-laden Air. In the following table, 
extracted from the same source as the last, similar facts are set 
forth for occupations in which there is special liability to injury 
from the inhalation of solid particles : — 



OCCUPATIO^^ AND INIORfALlTY. 



183 



Occupation. 


Phthisis and | 
Diseases of the | 
Respiratory 
System. ; 


Phthisis. 


Disca.ses 

of 
Respira- 
tory 
System. 


Diseases 

of 
Circula- 
tory 
System. 


Mortality 
Figure. 


Ratio. 


Mortality Figure. 


Agriculturist . 


221 


100 


106 


115 


83 


Ironstoue-miuer 
Carpenter 
Coal-miuer 
Corn Miller 
Baker, Confectioner 
Blacksmith 
Wool Manufacture . 
Tin-worker 

Carpet, Rug Manufacture . 
Bricklayer, Mason, Builder 
Cotton Manufacture 
Lead-worker . 
Chininey-swee]) 
Stone Quarrier 
Zinc-worker 

Iron and Steel Manufacture 
Gunsmith 
Copper-miner . 
Copjier-worker 
Lead -miner 
Glas.s JIanufacture . 
File-maker 
Tin-miner 

Cutler, Scissors-maker 
Potter, Earthenware 
Manufacture 


294 
326 
366 
366 

392 
392 
447 
451 
471 
476 
540 
545 
551 
576 
587 
645 
649 
678 
700 
705 
740 
825 
885 
900 

1001 


133 

148 
166 
166 
177 
177 
202 
204 
213 
215 
244 
247 
249 
261 
266 
292 
294 
307 
317 
319 
335 
373 
400 
407 

453 


90 

172 
97 
143 
185 
159 
191 
217 
226 
225 
202 
148 
260 
269 
240 
195 
324 
331 
294 
380 
295 
402 
508 
382 

333 


204 
154 
269 
223 
207 
233 
256 
234 
245 
251 
338 
397 
291 
307 
347 
450 
325 
347 
406 
325 
445 
423 
377 
518 

668 


84 
106 
120 
112 
130 
136 
131 
124 

87 
130 
152 
272 
142 
137 
126 
162 
153 
121 
186 
142 
157 
204 

95 
167 

227 



Dr. Ogle, in his remarks concerning the effects of ditst on the 
lungs in 1880-82, pointed out that the dust of coal and of Avood 
was the least injurious, while the dust of metals and of stone Avas 
the most injurious, flour dust and the dust given off and inhaled 
in textile factories occupying an intermediate position as regards 
injury to health. Dr. Tatham's figures, just given, on the whole 
confirm this generalization. The favourable position of coal- 
miners is particularly noteworthy. 

Effects of Chronic Lead-poisoning. Lead-poisoning is evi- 
denced particularly in the following occupations, the comparative 



184 



TITAL STATISTICS. 



mortality figures for plumbism being 211 for lead-Avorkers, 75 
for file-makers, 21 for plumbers, 18 for glaziers and painters, 17 
for potters, 12 for glass-makers, 8 for copper-workers, 7 for 
coach-makers, 6 for gasfitters and locksmiths, 5 for lead-miners, 
3 for printers, cutlers, and wool manufacturers, as compared with 
1 for all occupied males. This does not exhaust the evil, the 
figures under the head of urinary diseases, diseases of the 
nervous system and gout, shoAving a great excess in most of the 
above occupations. 

Effects of Alcoholic Excess. The death returns under the 
head of alcoholism are notoriously imperfect. Cirrhosis of the 
liver forms a better index of alcoholic excess. It is well known, 
however, that the persistent excessive consumption of alcoholic 
drinks damages most of the viscera of the body. Hence diseases 
of the nervous system, phthisis, urinary diseases, gout, and suicide 
are excessive in their incidence on the occupations in which 
alcoholic indulgence is common. In the following table the 
mortality of occupied males in 1890-92 at ages 25-65 years, 
from each cause of death, has been expressed as 100; and the 
mortality in each several industry has been reduced to a figure 
proportional to that standard. 





a S 

'o m >, 
^1° 


'o 

1 

< 


O 
S 


+3 

o 

a 


° m ■ 
m p C 
m ? 53 

5^^ 


§ 
"5 

m 




p 


Occupied Males 


100 


100 


100 


100 


100 


100 


100 


100 


Coachman, Cabman 
Costermonger . 
Coal heaver 
Fishmonger 
Musician 
Hairdresser 
Dock Labourer 
Chimney-sweep 
Butcher . 
Brewer 
Inn Servant 
Innkeeper 




153 
163 
165 
168 
168 
175 
195 
200 
228 
250 
420 
733 


215 
277 
223 
215 
223 
269 
400 
454 
269 
315 
815 
708 


122 
107 
137 

144 
141 
130 
96 
78 
207 
219 
230 
744, 


300 
150 

150 
450 
400 
150 

300 
500 
550 
600 


100 
170 
120 
109 
135 
109 
139 
100 
128 
152 
132 
195 


143 
100 
50 
150 
164 
250 
157 
221 
164 
121 
179 
229 


124 
239 
116 
86 
174 
149 
176 
141 
105 
148 
257 
140 


132 

171 
122 
120 
141 
78 
166 
144 
117 
190 
188 
220 



CHAPTER XVIII. 

MORTALITY FROM ZYMOTIC DISEASES. 

WE have in the preceding chapters shown the eftect produced 
by various social and other conditions on the general 
mortality. In the next place we must consider the mortality 
from individual diseases and from groups of diseases. In the 
first place, as to the methods of stating this mortality. This 
will vary according to the object in vieAV. (1) The first plan, 
useful for purely medical purposes, consists in stating the pro- 
portion of deaths to persons attacked by any given disease. 
Tliis method is of importance as indicating the degree of 
virulence of a particular disease, and l^ecause from the results 
thus obtained deductions can be drawn concerning the effect of 
a particular line of treatment. We may point out the liability 
of this method to error before passing on to the statement of 
methods usually adopted by vital statisticians. 

(rt) The number of facts manipulated is often so small as not 
to warrant exact conclusions. Thus in a small outbreak of 
enteric fever, investigated by the author, of 21 total cases, 
15 were treated either at home or in one public institution, 
while 6 were treated in another public institution. Of the 
former none died, while 2 of the latter proved fatal. The 
difference in fatality was almost certainly due to causes other 
than the methods of treatment, and any inferences as to skill 
of treatment would be altogether fallacious. Speaking generally, 
tlierapeutical results or etiological theories, advanced on the 
strength of iiercentages from a small numher of cases, must he 
accepted, with caution. (See also page 323.) 

(h) The two groups compared may have a different age and 
sex-constitution, and it is a notorious fact that the death-rate 
from nearly all diseases is largely influenced by these factors, 
and especially by age. 

Thus in typhus fever the percentage mortality (fatality) varies 

185 



186 VITAL STATISTICS. 

from 2-28 at ages 10-15, and 3-59 at ages 5-10, to 49-62 at 
ages 50-55, and still greater at higher ages. In enteric fever 
the fatality varies from 11-28 per cent, at ages 5-10, and 12-06 
under 5 years of age, to 26-61 at ages 40-45, and 45 per cent, at 
ages 55-60. (See pp. 237 and 606, Murchiso7i's Treatise on 
Go7itinuecl Fevers, Third Edition, 1884.) 

Similarly whooping-cough is much more fatal among female 
than among male children. Thus in 1881-90 the death-rate 
from this disease averaged 3672 per milKon female children 
under 5 years of age, as compared witli 3066 among male children 
at the same age. In the next group of ages 5-10 the death- 
rates per million living were 155 and 100 among female and 
male children respectively. 

(c) Ey splitting up the deaths at all ages into groups at different 
ages, the number of individual facts at each age is reduced, and 
thus tlie fallacy due to paucity of data may be introduced. This, 
however, is preferable to the lumping together of sets of facts 
which are not comparable with each other. In stating percentages, 
the number of fads on ivliich tliey are foimded sliould always he 
given, as their trustworthiness can then be gauged. 

{d) In the case of infectious diseases, the character of the 
particular e2Didemic must be taken into account. One epidemic of 
diphtheria may differ in virulence from another, and comparison 
betAveen methods of treatment in the two epidemics would be 
to that extent vitiated. Similarly, it would be unfair to compare 
the treatment at the beginning of an outbreak of cholera, when 
50 per cent, of those attacked commonly die, Avith the treatment 
in the later and milder period of the epidemic. 

(2) The mortality from any given disease or group of diseases 
may be stated as a proportion to the deaths from all causes. 
This method is, hoAvever, essentially fallacious, as it constitutes 
a ratio betAA^een tAvo factors, of AAdiich both are A^ariable, viz., 
the mortality from the specified disease, and the mortality from 
all causes. Dr. Kansome gives the foUoAving example of its 
fallacious character. Suppose a toAvn of 100,000 with 2000 
annual deaths, of which 500 are caused by phthisis. Here the 
general death-rate is 20 per 1000; the death-rate from phthisis 
is 5 per 1000 living, and the deaths from phthisis form one- 
fourth of the total deaths. In another toAvn, having the same 
population, the total deaths are 4000, and therefore the death- 
rate 40 per 1000 inhabitants; the deaths from phthisis are 
1000, and therefore the death-rate from phthisis is 10 per 



MORTALITY FROM ZYMOTIC DISEASES. 187 

1000; but the proportion of the phthisical to the total mortality 
is one-fourth, as before. In the second town, therefore, there 
is by the latter test apparently no worse condition, so far 
as phthisis is concerned, than in the first, though matters are 
really twice as bad. 

In annual reports of medical officers of health the zymotic 
mortality is frequently stated as a percentage of deaths from all 
causes. Thus, if in one year the zymotic mortality forms 11 
and in the next year 15 per cent, of the total mortality from 
all causes, it is evident that the relative mortality might be 
increased either by a diminution in total deaths or an increase 
in zymotic deaths, though the inference to be drawn in the two 
cases would he very different. 

It is occasionally convenient to know the percentage of deaths 
due to different causes, in order to estimate the relative magnitude 
of the different causes of death; but this method cannot be 
employed with propriety in comparing one community with 
another, or even in comparing the records of the same community 
in successive years. 

(.3) TJie deaths from each individual cause may he stated per 
thousand or per million of the entire population. 

Tables on this basis for the principal zymotic diseases will be 
found on p. xcvi. et seq. of the Ammcd Report of the Registrar- 
Ge7ieral, 1896, for the whole of England and Wales, and on 
pp. xx-xxvi. of the Annual Summary for 1896 for 33 great 
towns and 67 other large towns, or in the corresponding parts 
of the reports for other years. 

Here again the importance of stating the number of facts on 
which the death-rate is based must be emphasized. A single 
fatal case of diphtheria imported into a hamlet with 200 in- 
habitants M^ould mean a death-rate from that one cause alone 
of 5 per 1000, and if the rate were published apart from the 
data on which it was based, an erroneous impression would be 
produced. A single year's returns are apt to make a small 
district come out very badly or too favourably. 

As the age-constitution of the population varies but slowly, 
death-rates per 1000 of the entire population are sufficiently 
accurate for most purposes and for the majority of diseases. 
When, however, special accuracy is required, and always when 
dealing with certain diseases, 

(4) The deaths from each individual disease at a given age- 
group should he stated per 1000 of the population living at the 



188 



VITAL STATISTICS. 



same age-rjroup. Thus a comparison of the death-rate per 1000 
of entire population from measles in a residential suburb with 
the corresponding death-rate from measles in a thickly-populated 
artisan district would be unfair, owing to the higher proportion 
of young children in the latter, among whom measles is chiefly 
fatal. 

The method adopted in the Eegistrar-General's reports of 
stating the diarrhoeal death-rate in terms of the entire population 
is especially open to objection. This can be made clear by two 
examples. The death-rates in the first column of the following 
table are taken from the Annual Summary of the Registrar- 
General for 1896 ; the second column has been calculated by 



Place. . 


Deaths from Diarrhoea 


Per 1000 of 
Population. 


Per 1000 Births. 


Dover 

Hastings 

Percentage excess of Dover over 
Hastings 

Huddersfield 

Newcastle-on-Tyne .... 

Percentage excess of Newcastle over 
Huddersfield .... 


•42 
•26 


15-7 
14^1 


+ 61-5% 


+ 11-4% 


•26 
•51 


12-9 
16-4 


+ 96-1% 


-h27-l% 



Thus by the less exact method the percentage excess of Dover 
and NeAvcastle respectively is 61 '5 and 96^1 per cent., instead of 
11^4 and 27^1 per cent., as indicated by the method which more 
nearly approximates to the truth. About 80 per cent, of the 
total deaths from diarrhoea occur under one year of age; and if 
the deaths from diarrhoea in the third quarter of the year be taken 
as a more accurate index of the prevalence of epidemic diarrhoea, 
the proportion of deaths under one year of age is still higher, and 
their statement in terms of the number of births an even closer 
approximation to the truth. 



MORTALITY FROM ZYMOTIC DISEASES. 189 

Zymotic Death-rate. The term Zijinotir, w.as introJncod by 
Dr. Yaw, and it is practiciiUy so convenient that we propose to 
adhere to it, although Specific Febrile Diseases is perhaps a more 
correct designation. The diseases comprised under this head have 
such a varied origin, that a rate compounded of all of them would 
l)e of but secondary importance. Tlie Registrar-General gives the 
death-rate from the seven chief infectious diseases (small-pox, 
measles, scarlet fever, di])htheria, Avhooping-cough, fever, and 
diarrhoea), and tliis is usually described as the zymotic death-rate. 
As a test of sanitary condition, this rate possesses considerable 
value, which must not, however, be exaggerated. To l^egin with, 
the prevalence of such diseases varies greatly in different districts, 
according to the proportional number of young children in each, 
apart altogether from any differences in sanitary or social con- 
ditions. Then again, although whooping-cough and measles have 
a much greater effect in increasing the mortality than typhus and 
enteric fever, they are much less amenable to sanitary measures 
than the latter diseases. An accumulation of children unprotected 
by a previous attack of the two first of these diseases, along with 
a s])ell of severe weather, might cause a great increase of zymotic 
mortality in any given locality, without its being of necessity in 
a less healthy condition than another which had escaped. The 
zymotic death-rate should always be separated into its seven com- 
ponent parts, as well as stated as a whole. 

Periodicity in Epidemic Diseases. In stating annually the 
mortality from some of the infectious diseases, it sliould be 
remembered that their infrequent appearance in the death-returns 
may be caused by the fact that there are but fcAV in the population 
wlio have not purchased immunity by a previous attack. After a 
large epidemic of measles, or whooping-cough, or scarlet fever, 
there is often a lull for several years. Dr. Ransome has inves- 
tigated the influence of cyclical waves, which appear to be 
independent of the accumulation of unprotected persons. From 
the Swedish tables of mortality (Epidemiological Society Trans- 
actions, 1881-82) he has constructed charts, Avliich show that, 
in the case of scarlet fever, there is not only a short cycle of 
from four to six years, but also a long undulation of from 1.5 to 
20 years or more, " which may be likened to a vast wave of disease 
upon which the lesser epidemics show like ripples upon the surface 
of an ocean swell." 

Dr. Whitelegge, in extending Dr. Ransome's researches on 



190 



VITAL STATISTICS. 



periodicity, has pointed out certain distinctive features between 
the shorter and longer cycles. The shorter or "superadded" 
disease waves are not attended by any regular and progressive 
increase and subsequent decrease of virulence. They are, in fact, 
waves of mere jDrevalence, as in epidemics due to infected 
milk or water. The longer or fundamental disease waves are 
characterized, on the other hand, by an increase both of prevalence 
and severity, as shown by increased fatality of the disease and a 
tendency for persons to be attacked at ages which are usually 
little prone to the disease in question. 

Measles has been shown by Dr. Whitelegge to be characterized 
by minor and major epidemics, the former "occurring every year 
or two, and in a sense mechanically," and the latter occurring at 
longer intervals, and possibly due to progressive alterations in the 
intensity of the measles virus. 

Average Death-rates. In the following table the average death- 
rates from certain diseases or groups of diseases are given : — 

Annual Deaths per 1,000,000 persons living. 





1871-80. 


1881-90. 


1891-95. 


Small -pox ...... 


234 


45 


20 


Measles 








378 


440 


408 


Scarlet Fever . 








716 


334 


182 


Diphtheria 








121 


163 


253 


Whooping-cough 








512 


450 


398 


Typhus . 








57 


14 


4 


Enteric Fever 








322 


196 


174 


Continued Fever 








103 


25 


8 


Diarrhoeal Diseases 






935 


674 


652 


Cancer .... 






468 


589 


712 


Phthisis 






2116 


1724 


1464 


Other Tubercular Diseases 






747 


696 


660 


Diabetes 






38 


57 


69 


Diseases of the Nervous System 




2789 


2592 


2288 


„ „ Circulatory System 


1339 


1576 


1677 


„ „ Respiratory System 


3899 


3729 


3747 


„ „ Digestive System 


1165 


1104 


1116 


„ „ Urinary System 




350 


435 


453 


Puerperal Fever, Child-birth . 




167 


153 


167 


Violence ..... 




733 


648 


663 


All other and unstated Causes 




4083 


3436 


1623 


AllC 


auses 




• 


21272 


19080 


18738 



18o0 



1860 



1870 



1880 



1890 




Fig. 22. 
Amnial Dt';itli-nUe tVoiii Mea^iles an*! W}i..i.i.iug-c-oiigh, 1847-9g 



, per million of population, in England and Wales. 



MORTALITY rEO:\r ZYMOTIC DISEASES. 191 

Tlie above table is useful to show the relative death-rates from 
certain diseases, and to indicate tlie general tendency towards 
increase or decline in mortality from them. In accurate investiga- 
tions into the prevalence of infectious diseases, especially those 
dealing with limited districts, average death-rates should be 
eschewed, the death-rate for each year being plotted out in 
diagrammatic form, so that the exact course of the disease may 
be traced. It may be desirable occasionally to plot out the 
monthly or quarterly incidence of a disease. By this means the 
influence of an epidemic in disturbing the usual seasonal incidence 
of eacli infectious disease can be detected. 

It is particularly dangerous to compare the mean death-rate of 
two cities or other places for periods of years which do not coin- 
cide in the two instances. Even when an average is struck for 
the same series of years, there remains the fallacy that one place 
may have happened to have, say, three epidemics, and another 
four during tlie given term of years. It might thus happen, for 
instance, that if two or three additional years had been added to 
the series, the jDlace of the two cities would have been reversed as 
regards their average death-rate from the disease in question. 

Measles. The death-rate from this disease in England has varied 
between 1847 and 1896 from 602 per million persons living in 
1887 to 257 in 1875, averaging 441 in 1881-90. In London 
it has varied from 884 in 1858 and 942 in 1864 to 246 in 1852, 
averaging 636 in 1881-90. 

Fig. 22 shows that the average annual mortality from measles 
has not fluctuated greatly in the course of the last fifty years. It 
is more fatal in urban than rural districts. The highest mortality 
from measles is at the ages 0-5. In the decennium 1881-90 it 
was 3131 per million persons living in England at these ages, 
only 271 in the next age-period 5-10, and 23 in the age-period 
10-15. The death-rate per million living at each year of age 
under 5 in 1881-90 was 3365 under 1 year, 2916 at age 2-3, 
1684 at age 3-4, and 1031 at age 4-5. It is evident that the 
higher death-rate at the younger ages might be due to the 
larger number attacked at these ages, or to a greater fatality 
among those attacked, or to both these combined. The data for 
elucidating this point are scanty, being only obtainable for districts 
in which measles is compulsorily notifiable. Even in such dis- 
tricts it is more likely in the case of measles than of other notifi- 
able diseases that cases escape notification, oAving to the lack of 



192 



VITAL STATISTICS. 



medical attendance in a large proportion of cases. In Edinburgh 
in 1880-89 the fatality from measles A^aried from 5-9 per cent, in 
1880 to 1*5 per cent, in 1881, averaging ovl per cent, for the ten 
years.* The cases are not classified according to age. 

Dr. T. Thomson! gives the statistics for a certain district having 
an estimated mean population March, 1892, to March, 1894, of 
35,G06, during nearly the whole of which time measles was 
epidemic in the district. 



Age-groups. 


Estimated 

mean 
Population. 


Measles. 


Attack-vato 
per 1000 
living. 


Deatli-rate 
per 1000 
living. 


Fatality per 

1000 

attacked. 


At all ages 


3560(3J 


28 


1-7 


61 


0-1 
1-2 
2-3 
3-4 
4-5 


1155 

974 

1028 

1000 

951 


72 
119 

172 
162 
170 


6-9 

23-6 

17-5 

8-0 

2-6 


96 

197 

102 

49 

15 


All ages under 5 
5-10 
10 and upwards 


5108 

4530 

25968 


137 
62 
0.75 


11-6 
0-7 
0-0 


85 

11 





The population figures for the second year of life indicate some 
confusion of the census figures on which they are based, and 
consequently throw a little doubt on the rates for the second year 
of life. The figures as they stand show that the main incidence 
of deatlis is on the second year of life, while the main incidence 
of affacks is on the third, fourth, and fifth years of life. It 
follows that the fatality from measles is much higher in the 
second than in any of the three succeeding years. 

* Ten Years' Compulsory Notification of Infectious Disease in Fdijihurgh. 
By Dr. H. Littlejohn, p. 138. 

t Supplement to the Twenty fourth Annual Eeport of the Local Government 
Board, p. 138. 

J The population figures are given, but to economize space not the number 
of cases and deatlis. The latter can obviously be calcuUited, tlie population 
and the rates per 1000 being given. 



MORTALITY FROM ZYMOTIC DISEASES. 193 

The death-rates for the two sexes show that luuku- ;! the deatli- 
rate from measles is higher among males (3271 in lSSl-90) 
than among females (2992), wliile at the age group 5-10 the 
death-rate among males is 2G2, among females 280, and at 10-15 
it is 19 and 2G per million living respectively. 

Tlie iniluence oi season on the mortality from measles in London 
is shown in Fig. 14. There are two maxima in eacli year, viz., 
in May and June, and in Novemher to .lanuary, the latter gi'eater 
tlian tlie former. In many other towns, e.g., in Paris, IJerlin, 
and New York, the winter rise is small, the greatest incidence of 
the disease being in June. 

Scarlet Fever. The death-rate from this disease was stated 
separately from that for diphtheria for the iirst time in 1855 
in the Registrar-General's rejiorts. 

In Fig. 23 the course of the two diseases in England can be 
traced. As it was thought desirable to show the combined 
prevalence of the two diseases, a diagram drawn to scale was 
made for scarlet fever, and then a second diagram for diphtheria 
2^his scarlet fever, the space between the two curves then repre- 
senting the annual death-rate from diphtheria. The same method 
is adopted in Figs. 26 and 27. The death-rate from scarlet 
fever has varied from 1478 per million persons living in 1863, 
and 1446 in 1870, to 149 in 1895. 

The average death-rate from scarlet fever in 1881-90 was 346 
per million males and 322 per million females. At age 0-5 it 
was 1712 and 1627 per million living in the male and female sex 
respectively; at age 5-10, 758 and 765; at age 10-15, 148 and 
158; at age 15-20, 43 and 40 respectively; still lower at higher 
ages. At all ages in the aggr(>gate, and in children under 10 
years of age, scarlatinal mortality is higher among males, ])ut at 
higher ages the female rate is higher. Scarlet fever is like 
diphtheria, and is unlike whooping-cough, in being less fatal to 
infants under one year of age than to those in their second, 
third, fourth, or fifth years. 

The rapid decline in the registered mortality from scarlet fever 
might be caused by diminished prevalence or diminished virulence 
of the disease. The question is, whether the diiferences shown 
above are due to differences of prevalence or differences of ease 
■inortality (fatality) 1 The Ammal Report of the Ik'iiistrar-General 
for 1886 gives the figures in column (a) of the following table, 
which bear on this jioint. They embody the facts as to tlie age, 
o 



50 

1800 
1700 

50 

1600 

50 

1500 

50 
1400 




Fig. 23. 



Annual Death-rate per Million of Population from Scarlet Fever and 
Diphtheria, 1847-96. 

The dotted part of the diagram gives the Death-rate from Diphtheria, the part indicated 
by diagonal lines the Death-rate from Scarlet Fever, the sum of these two the combined 
Death-rate from Scarlet Fever plus Diphtheria. 



MORTALITY FROM ZYMOTIC DISEASES. 195 

sex, and result of 17,795 cases of scarlet fever in the metropolitan 
fever hospitals during the twelve years 1874-85, and in addition, 
the official reports for Christiania, in Norway, of 5000 cases 
which occurred there in 1870-72. It was necessary to include 
these, because the returns of the London hospitals did not at 
that time diiferentiate each year of the 0-5 period, during whicli 
the prevalence of scarlet fever is at its maximum. As the case 
mortality in Christiania for the aggregate 0-5 period Avas nearly 
the same as that of the corresponding period in London, it was 
fairly assumed that the rates for individual years Avere likewise 
similar. 

In column (h) of the same table are stated the fatality at each 
age of 39,253 male and 42,352 female cases of scarlet fever 
admitted to the metropolitan hospitals in the years 1892-97. 



Fatality per 100 Cases of Scarlet Fever. 



Age. 


1S74-85. 


1892-97. 


1874-85. 


1892-97. 


Males. 
(a) (b) 


Females. 
(a) (6) 


0-1 .. . 
1-2 .. . 
2-3 .. . 
3-4 .. . 
4-5 .. . 


39-5 
38-4 
25-5 

18-4 
13-0 


24-8 
20-5 
15-4 
11-2 
8-1 


44-2 
34-6 
22-6 
17-4 
11-2 


27-1 
20-4 
15-0 
11-3 
6-8 


Total, 0-5 


24-1 


12-8 


21-7 


12-0 


5-10 . 
10-15 . 
15-20 . 
20-25 . 
25-35 . 
35 and upwards 


10-6 
5-6 
4-0 
3-9 
7-5 
8-5 


3-1 
1-3 
1-5 
1-2 
1-7 
4-9 


9-7 
5-3 
3-4 
3-2 
4-3 
6-5 


3'0 
1-1 
1-5 
1-7 
1-3 
2-6 



The same figures also shoAV that at each age and group of 
ages the fatality of scarlet fever has declined to a remarkable 
extent. As the death-rate and the fatality from scarlet fever 
both decline with advancing years, it is clear that the longer 



196 VITAL STATISTICS. 

an attack is deferred the less likely is it to occur at all; and 
that even if it occur eventually, the less likely is it to end 
fatally. 

There are no figures based on the compulsory notification of 
scarlet fever, twenty or thirty years ago, to enable a certain con- 
clusion to be reached as to the question previously asked ; but, 
on the whole, it seems clear that there has been a real "change 
in the constitution" of scarlet fever, and that if there is 
diminished prevalence of this disease it is subsidiary in im- 
portance to its diminished fatality. 

Diphtheria. This disease was only separated from scarlet 
fever in the Registrar-General's returns in 1855, and there is 
little doubt that many deaths are even now returned as ulcerated 
throat, quinsy, croup, laryngitis, or membranous laryngitis, which 
should be entered as diphtheria. Elsewhere* I have discussed 
the influence of these changes of nomenclature, and have shown 
that by plottmg out the annual death-rate from croup, plus 
diphtheria, we obtain approximately accurate results. It is 
possible that in a given diagram thus obtained, the amount of 
diphtheria may be understated ; but the teaching of the diagram, 
as to which are the epidemic and which the inter -epidemic 
years, can be confidently accepted. It is on the position rather 
than on the height or depth of the crests and troughs of the 
epidemic waves that the main teaching of such curves depends, 
and these may be regarded as absolutely accurate. 

The variations in the English death-rate from diphtheria since 
1855 can be seen in Fig. 24. The highest was 517 per million 
living in 1859, and 318 in 1893; the lowest (omitting the three 
years 1855-57, in which there was probably still some confusion 
with scarlet fever) 93 in 1872. In London the highest death- 
rate per million living since 1859 was 761 in 1893, and the 
lowest 80 in 1872. 

In the decennium 1881-90 the male death-rate at all ages in 
England and Wales averaged 158, the female 167 per million 
living, being 688 and 693 in the male and female sexes at ages 
0-5, 373 and 474 at ages 5-10, 84 and 115 at ages 10-15, and 
35 and 37 at ages 15-20. 

Diphtheria agrees with scarlet fever in being less fatal to 

* Epidemic BipJitheria : A Research on the Origin and Spread of the 
Disease from an International Standpoint. Swan Sonnenscliein & Co., 1898. 




Fig. 24, 

Yearly Death-rate from Diphtheria (black), Croup (mottled), and Laryngitis 
(clear) ; in {a) England and Wales, {b) London. 



198 



VITAL STATISTICS. 



infants in their first year of life than in any other year of the 
first five. 

The folloAving table gives the experience as to the fatality from 
diphtheria among 11,553 male and 13,861 female patients ad- 
mitted into the Metropolitan Asylums Board's Hospitals in the 
years 1888-97:— 



Ages. 


Fatality per cent. 


Males. 


Females. 


Total. 


Under 1 . 
1-2 . 
2-3 . 

3-4 . 
4-5 . 

Total under 5 . 
5-10 . 
10-15 . 
15-20 . 
20-25 . 
25-35 . 
35 and upwards . 


481 
50-2 
42-3 
367 
30-4 


52-6 
50-5 
39-3 
33-9 
31-3 


50-1 
50-3 
40-8 
35-3 
30-8 


38-9 
21-4 
8-7 
5-2 
4-7 
5-5 
10-9 


37-2 
23-2 
8-5 
4-2 
3-6 
4-3 
8-5 


38-0 
22-3 
8-6 
4-6 
4-0 
4-6 
9-4 



The fatality of diphtheria has not varied so enormously as that 
of scarlet fever. There are no English figures stretching over a 
sufficient length of years to prove this statement, but the follow- 
ing curve derived from the experience of Copenhagen for the 
years 1855-94, in which city compulsory notification of infective 
diseases has been long established, shows that the sickness-rate 
and the death-rate from diphtheria closely follow each other. To 
bring out this point a method has been employed which is most 
useful in many similar inquiries. The average attack-rate (5 '88. 
per 1000) and death-rate ('78 per 1000) for the entire period is 
calculated, and then the percentage deviation of each year's rate 
from the mean having been ascertained, these deviations are 
plotted out as shown in Fig. 25. 

It will be observed that although the attack-rates and death- 
rates do not deviate greatly from one another, the fatality of the 
disease increased somewhat during the epidemics culminating in 
1865_^and in 1879, while during the epidemic culminating in 1890 
the casesjncreased in a slightly higher proportion than the deaths. 



1890 



1880 • - 



1870 



186C- 




200 VITAL STATISTICS. 

The pathogenesis and epidemicity of diphtheria are discussed in 
detail in the author's " Epidemic Diphtheria," to which reference 
must be made for further particulars. 

Whooping-cough. The annual death-rate from this disease in 
England can be seen in Fig. 22. It has varied since 1847 betAveen 
736 per million living in 1866 and 316 in 1895. In the years 
1881-90 it averaged 418 for males and 480 for females of all ages. 
Under 5 years of age the male death-rate per million was 3066, 
the female 3672; at ages 5-10 it was 100 and 155; at ages 10-15 
it was 3 and 5 respectively. The death-rate per million living in 
1881-90 in each of the first five years of life beginning with the 
first were 7085, 5490, 2168, 1186, and 641 respectively. 

Fever. Under this head are included typhus fever, enteric or 
typhoid fever, and simple and ill-defined forms of continued fever. 
Typhus and typhoid fevers were definitely recognized and differen- 
tiated as separate diseases as early as 1849-51 in the Avritings 
of Jenner, and near the same time by A. P. Stewart and a 
few others. It was not, however, until 1869 that the three 
headings of typhus, enteric fever, and simple and ill-defined fever 
were commenced in the oflicial returns. The course of the diseases 
enumerated above can be seen in Fig. 26. 

In 1847 the death-rate per million from "fever" was 1807, 
declining to 652 in 1860, and to 895 in 1868. It is probable that 
in these earlier years defective diagnosis caused many erroneous 
entries under this head of what Avould now be recognized as 
tubercular meningitis, general tuberculosis, pneumonia, etc. This 
is supported by the course of the curve in Fig. 26, which shows 
the gradual extinction of simple and ill-defined continued fever, 
owing to its gradual transference to the Uyo other headings. The 
rapid diminution of typhus is shown by clinical evidence to be 
real, this disease tending to become extinct in connection Avith 
improved sanitation. Thus the death-rate per million living from 
typhus dechned from 57 in 1871-80 to 14 in 1881-90, and 4 in 
1891-95. 

There can be no doubt also that the reduction of typhoid fever 
is in the main a real one. In 1871-80 the death-rate from this 
disease Avas 322, in 1881-90 it Avas 196, and in 1891-95 it Avas 
174 per million living. The decline at each age-period is a matter 
of some importance, and Ave therefore give the folloAAdng table 
shoAving the rates and the percentage decline for each sex. 




Fig. 26.— Annual death-rate from simple and ill-defined, typhus, and enteric fevers, 1S69-9 



202 



VITAL STATISTICS. 



Enteric Fever — England and Wales. 









Males. 


Females. 




Death-rate 


per million. 


Decline 
per cent. 


Death-rate 


per million. 


Decline 
per cent. 












1S71-S0. 


1881-90. 




1871-80. 


1881-90. 




All ages 


325 


211 


35 


320 


182 


43 


0- . 


396 


131 


67 


404 


128 


68 


5- 






308 


170 


45 


364 


189 


48 


10- 






273 


191 


30 


350 


225 


36 


15- 






376 


298 


21 


436 


280 


36 


20- 






430 


336 


22 


334 


233 


30 


25- 






309 


272 


12 


280 


196 


30 


35- 






258 


201 


22 


238 


164 


31 


45- 






273 


176 


35 


230 


135 


41 


55- 






290 


165 


43 


247 


122 


50 


65- 






340 


132 


61 


255 


98 


61 


75 & upwards 


259 


71 


73 


187 


55 


71 



The most striking feature of this table is, that the mortahty 
from enteric fever has decreased much more under 10 and over 
55 years of age than at the intermediate ages. The inequality of 
the decline of the fever-rate at different ages is probably largely 
owing to greater accuracy in diagnosis in regard to the very young 
and old, who were formerly said to die from "fever" or typhoid 
fever, but who are" probably now grouped more accurately under 
other headings. 

After ample allowance for this source of error, there has still 
been an enormous reduction of fever at all ages. Nor can the 
reduction of mortality be ascribed to the prevalence of a milder 
type of disease. This is shown by the folloAving figures from the 
experience of (a) the London Fever Hospital (Murchison) in 
1848-57, and of the Metropolitan Asjdums Board's Hospitals (b) 
in 1871-97, and (c) in 1897. 



MORTALITY FROM ZYMOTIC DISEASES. 203 











Fatality per 100 cases treated at 
each age-group. 


Ages. 


(ft) In the 
years 1848-57. 


(h) In the 

years 1871-97 

(total cases 

11,148). 


(c) In the 

year 1897 

(total cases 

664). 


Under 5 . 


12-1 


12-9 


7-1 


5- 








11-3 


8-9 


7.7 


10- 








12-9 


13-0 


9-5 


15- 








15-5 


17-5 


20-8 


20- 








20-4 


20-3 


18-8 


25- 








20-5 


22-9 


29-9 


30- 








25-6 


24-9 


34-0 


35- 








26-4 


27-2 


27-3 


40- 








26-6 


24-9 


25-0 


45 and upwards 




19-6 


33-6 


23-1 


All Ages . 


17-3 


17-3 


18-7 



The decline in mortality from enteric fever must therefore be 
clue chiefly to its diminished prevalence. 

The following table shoAvs the attack-rate and death-rate per 
100,000 living from enteric fever for the entire population of: 
London at each age-i:)eriod in 1896 for the two sexes. 









Attack-rate. 


Death-rate. 

• 


Fatality (Case- 
Mortality) per cent. 




Males. 


Females. 


Males. 


Females. 


Males. 


Females. 


All ages . 


85 


61 


17 


10 


19-6 


16-0 


0-. 


38 


31 


6 


5 


15-2 


17-1 


5-. 






102 


81 


12 


7 


12-0 


8-7 


10-. 






131 


104 


13 


11 


9-9 


10-5 


15-. 






138 


95 


27 


18 


19-9 


18-7 


20-. 






117 


80 


26 


13 


22-3 


16-7 


25-. 






107 


70 


22 


12 


20-6 


17-3 


35- . 






60 


44 


19 


9 


321 


20-8 


45- . 






36 


29 


14 


6 


38-5 


20-3 


55 and upwards 


21 


10 


9 


4 


41-7 


43-5 



204 



VITAL STATISTICS. 



The liability to attack is seen to be greater at all ages in males 
than in females. The greatest liability to attack is between the 
tenth and twenty-fifth years of age. The fatality is higher at 
most ages in males than in females. 

Further particulars as to the case-rate from notifiable diseases, and as 
to variations of fatality, will be found on p. 337. 

Diarrhoea. Diarrhoea is the name of a symptom, not of a 
disease. It represents the residue after fatal cases, in which 
diarrhoea was the most prominent symptom, have been relegated 
to the disease which caused the diarrhcBa. The Registrar-General 
includes dysentery under this head, but true dysentery is noAV 
unknown as a disease having its origin in this country. Many 
cases which were formerly entered as diarrhoea now appear as 
enteritis or gastro-enteritis. Thus Dr. L. Parkes {British Medical 
Journal, May 28, 1898) has shown that in London the following 
change in the proportion of deaths at three age-periods to total 
deaths from the same cause at all ages has taken place. 

Percentage of Deaths at three Age-periods to Total Deaths. 



Years. 


Diarrhoea and Cholera. 


Enteritis. 


Under 1. 


1 to5. 


Over 5. 


Under 1. 


1 to 5. _ 


Over 5. 


1861-5 . 
1896-7 . 


62 
79 


20 
13 


18 
8 


30 

68 


12 
13 


58 
19 



Similarly, if the number of deaths registered as due to enteritis 
be stated in relation to every 100 deaths from diarrhoea and 
cholera, the proportion will be seen to have increased from 
11 per cent, in 1861-65 to 52 per cent, in 1896-97. It is 
uncertain how much of what is now returned as enteritis would 
have been formerly entered as diarrhoea, but the rapid increase 
of the death-rate from enteritis since 1877, shoAvn in Fig. 27, 
is very suggestive. 

The average annual death-rate from diarrhoea! diseases (in- 
cluding cholera) Avas 1076 per million living in 1861-70, 935 
in 1871-80, 674 in 1881-90, and 652 in 1891-95. The death- 
rate in 1881-90 per million living at each age-period was 4346 
under 5, and 2581 at 75 and over. These diseases are, therefore. 







^— rr 




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Fig. 27. 

Death-rate per Million of Population from Diarrhoea and Cholera (diagonally marked) 
and from Enteritis (marked by dotted lines). 



206 VITAL STATISTICS. 

most fatal at the extremes of life. This is especially true for the 
first year of life, in which the death-rate per million living in 
1881-90 was 16,044, that in the fifth year being only 145. 

The connection between the temperature of the air and the 
prevalence of diarrhoea is shown in the annexed diagram. 

Fig. 28, from an earlier edition of this work, is introduced 
partly for critical purposes. A more exact method and freer from 
fallacies would have been to work out the percentage deviation of 
each week's temperature during 1887 from the corresponding 
week's temperature for a series of years, and similarly to work 
out the percentage deviation of each week's diarrhoeal death-rate 
from the corresponding average weekly death-rate in a series of 
years, and then to plot out the two series of figures (which 
would now be on a corresponding scale) in a diagram. 

Diarrhoea being eminently an infantile disease, so far, at least, 
as it is fatal, and in fact being almost synonymous with epidemic 
diarrhcea, it would be preferable to state it in terms of the 
number of births (p. 188). By this means, a portion of the 
discrepancy in the death-rate from diarrhoea in great towns is 
removed. Considerable differences still remain when this correc- 
tion has been applied. These differences are partly due to the 
varying presence of insanitary conditions, es2Decially those con- 
nected with pollution of the soil and the atmosphere with excre- 
mental matter ; but social reasons also have undoubtedly a great 
influence, as the occupation of the mothers, the varying amount 
of feeding by hand, etc. The prevalence of diarrhoea is a matter 
of great importance, and ought to receive further elaborate and 
combined investigation by skilled observers. 



DIAGRAM SHOWING WEEK 
COMPARED WITH i 


.Y 


MORTAL 
WEEKLY 


TYfrom DIARRHIA in LONDON DURIN 
ELDCTUATIONSofMEAN TEMPFRATll 


G 1887, 

^E ^- 


520 

^ 500 

I 

i 400 

S 4G0 

O 440 

5 420 

70 400 

63 380 
66 360 

64 340 

62 320 

60 300 

58 280. 
M 

I 

56 2 260 
O 

54 O 240 

52 1220 

2 
50 200 

48 180 

46 160 

44 140 

42 120 

40 100 

38 80 

36 60 

34 40 

32 20 

30 


























p 












— 










































































































Line of Mean Temperature ■ 

Line of Weekltt Cases of Dinrrhcen^^ 






































h 




































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52WEEKSQf lan 


-.; 4 G a 10 12 14 IG la 2022 24 26 28 so 32 31 36 


33 40 42 44 4G 43 50 5?| 




JAN. 1 FEB. iMAnCHi APRIL | MAY | JUNE | JULY | AUG. | SEP. | OCT. | NOV. 


DE 


^-i 



Fig. 28. 



CHAPTEE XIX. 

SMALL-POX AND VACCINATION. 

PROBABLY no department of vital statistics is so important 
as that which deals with small-pox and vaccination. As 
certainly, in no department of medicine has so large an appeal to 
figures been made, and in none have the deductions from figures 
been so contradictory, in a large measure owing to the intense 
mental bias with which this subject has been taken up by those 
whose chief anxiety appears to be to mould the figures so as 
to fit in with their preconceived prejudices. There has not only 
been incompetence and ignorance on the part of many anti- 
vaccinators who have dealt with vaccination and small-pox, but 
in some cases culpable misconduct in dealing with statistics. 

The Royal Commission on Vaccination have issued six enormous 
volumes of evidence and nine further volumes of reports of 
special inquiries made on behalf of the Commission. The final 
report of the Royal Commission, published in August, 1896,* 
comprises an excellent summary of the main facts and arguments 
relating to vaccination from every standpoint, and is essential for 
all who wish to obtain a grasp of the subject. The same volume 
contains the dissent of Dr. Collins and Mr. Picton, two members 
of the Commission, from the report, embracing practically every- 
thing that can be said on the anti-vaccination side. The review 
of the dissentients' statement by Dr. McVailf exposes in a 
masterly fashion the errors into which Messrs. Collins and Picton 
had fallen. The study of the preceding volumes will enable the 
intelligent reader to expose with ease the fallacies contained in 
the anti-vaccination pamphlets by Russell, Paul, and others. 

It is impossible here to more than summarize some of the chief 
facts of the subject and to indicate the chief errors, which have 
an incidental value as instances of statistical fallacies. 

* Eyre and Spottiswoode, Is. lOd. 
t P. S. King and Son. 

208 



SMALL-POX AND VACCINATION. 



209 



One of the chief errors has been to give avcrap,e death- 
rates for small-pox for series of years. The dangers of such 
average death-rates have been already emphasized (see p. 191). 
A glance at Fig. 29 will show how very easy it would be, 
esj)ecially in its earlier portion, to arrange the death-rates in 
groups of years, so that eitlier a reduction or an increase of 
small-pox mortality could be displayed in contrasting two con- 
tiguous periods. 

The death-rate from small-pox per million inhabitants in 
England has varied since 1847 from 1 in 1889-90 to 1012 in 
1871. The epidemic peaks since 1847 have occurred in the 
following years: 1847 (507), 1852 (401), 1858 (329), 1864 (.364), 
1871 (1012), 1877 (173), 1881 (119), 1885 (104), 1888 (36), 
1893 (49). In London the death-rate from small-pox has varied 
since 1848 between in 1889 and 7912 in 1871. The epidemic 
peaks have occurred in the following years: 1848 (1620), 1852 
(1159), 1855 (1039), 1859 (1158), 18(33 (1996), 1866 (1391), 1871 
(7912), 1877 (2551), 1881 (2367), 1885 (1419), 1893 (206). 

During 1896, 541 deaths in England and Wales were referred 
to small-pox, corresponding to a rate of 1'8 per million, com- 
pared with rates of 7, 27, and 49 in the three preceding years. Of 
the total 541 deaths from small-pox, 443 occurred in the registra- 
tion district of Gloucester. During the first half of 1896 the 
mortality of this city was increased, on account of small -pox 
alone, by 143 per cent. 

Although average death-rates for groups of years should not 
be considered alone, they may serve to indicate, without fallacy, 
if due precautions are taken, the trend of a particular disease, and 
for this purpose the following figures are useful : — 

Death-rate per Million prom Small-pox in England and Wales. 



Period. 


Persons. 


Males. 1 Females. 


Remarks, 


1861-70 
1871-80 
1881-90 
1891-95 


160 
234 

45 
20 


179 ' 142 

265 1 205 

52 38 


two epidemics, 
two epidemics, 
two epidemics, 
one small epidemic. 



The decrease in the death-rate from small-pox has until recent 
years been much greater in the provinces than in London, 
probably owing rather to the more frequent opportunities of 
infection in the latter than to any other cause. Thus in 1838-42 







J 8 40 



^1850 



*'18G0 



-'1870 



1880 



1890 



SMALL-POX AND VACCINATION. 211 

the death-rates per million living in England as a whole and in 
London respectively were 755 and 547, while in 1880-84 they 
were 244 and 34. In 1891-95 the death-rate from small-pox in 
London has only averaged 19 per million, as compared with 
20 in the Avholo of England. There can he little doul)t that the 
greatly imi)roved isolation accommodation for sm;dl-pox patients, 
in hospitals remote from centres of popnlation, is chielly re- 
sponsiljle for this great improvement in the metropolis. The 
clHciency of hospital isolation as a means of preventing epidemic 
small-2)ox in a community of which the largest })roportion has 
been vaccinated is one thing; it is quite another thing in an 
unvaccinated community. In view of the extreme infectiousness 
of the disease, it is more than doubtful if isolation and the 
collated measures would suffice to prevent epidemic small-pox in 
the absence of vaccination. 

Small-pox in the Pre-registration Period. Fig. 29 sIioavs that 
thei'c has been a decrease of small-pox mortality during the period 
for which there are official records in l^ngland. A study of 
small-pox, which is conlined to these sixty years, tloes not, however, 
give an adequate conception of the remarkable fall in small-pox 
mortality which has occurred. The work of vaccination in 
reducing small-pox was in a large measure accomplished by the 
middle of the nineteenth century, and since that time there has 
been much less scope for diminution. This will be clearly seen 
from the diagram relating to London, which faces p. G of Dr. 
IMcVail's Vaccinafion VimUcated (Cassell and Co., 1887), which, 
although published before the issue of the report of the Royal 
Commission on Vaccination, still remains an authoritative book on 
the subject. Small-pox reached its highest point in 179G (two 
years before the date of Jenner's "Inquiry"), Avhen 18^ deaths 
out of every 100 total deaths were caused by small-pox. In tlie 
pre-vaccination period small-pox was nine times as fatal as measles 
and seven and a half times as fatal as whooping-cough (McVail). 
Under vaccination it has sunk to an insignificant position when 
compared with these diseases. 

The Epidemic of Small-pox of 1870-73. Dr. Guy applied 
the term epidemic to any outbreak causing one-tenth or more 
of the total deaths from all causes in any year. He found that 
in London there were ten such epidemics of small-pox in forty- 
eight years of the seventeenth century, twenty -nine in the 



212 



VITAL STATISTICS. 



eigliteentli century, and none in the nineteenth century. If the 
standard be reduced to 7| per cent, of the total deaths, then 
fourteen epidemics occurred in the seventeenth century, sixty in 
the eighteenth, four in the nineteenth (McVail, oj). cit., p. 44). 
The above figures relate to London. The worst year under 
obligatory vaccination in London was 1871, in which barely 4|- 
per cent, of the total deaths were due to small-pox, a proportion 
which was exceeded in the eighteenth century ninety-three times. 
The 1870-73 epidemic, notwithstanding its comparatively small 
magnitude, has been frequently employed to show the inutility 
of vaccination. From 1847 to 1853 vaccination was optional; 
between 1854 and 1871 it was obligatory, but not efficiently 
enforced; from 1872 onwards it was obligatory, and more 
efficiently enforced by vaccination officers until recent years, 
in which the enforcement has become gradually relaxed in many 
districts. If we waive for the moment our objection to death- 
rates for groups of years, and contrast the death-rate in the 
five years 1865-70 with those in the two 5-year periods 1871-75 
and 1876-80 (1871 being the maximum epidemic year, and the 
year preceding that in which the more rigid Vaccination Act came 
into operation), we find that in the former period the death-rate 
from small-pox was 105, and in the latter periods 411 and 78 
per million persons in England and Wales. The Vaccination Act 
in question was directed towards securing infantile vaccination. 
It will be interesting, therefore, to observe the distribution of 
the above death-rates according to age. This is shown in the 
followinsc table : — 



Death-rate from Small-pox 
per million living. 


1S65-70. 


1871-75. 


1S76-S0. 


At ages under 5 

5-10 years 
10-15 „ 
15-25 „ 
25-45 .„ 
45 years and upwards 


413 
97 
32 
73 
60 
25 


937 
524 
234 
428 
351 
136 


145 
73 
52 
89 
82 
34 


At all ages * 


105 


411 


78 



* In the above table the average death-rates have, for the sake of con- 
venience, been obtained by the less accurate method of adding together the 
death-rates given on p. 155 of the final report of the Royal Commission on 



SMALL-POX AND VACCINATION. 213 

It will be seen that in the licriod 1871-75, during most of 
which small-pox was epidemic, a period including at least one 
year in which vaccination was not efficiently enforced, the death- 
rate under 5 years of age was only two and a quarter times 
as high as in 1865-70 (this period also includes one minor 
epidemic year), while the death-rate at other age-periods was five 
to seven times as high as that in the earlier years. In the next 
period (1876-80) no epidemic occurred, and the death-rate under 5 
was only about one-third the corresponding death-rate in 1865-70, 
while at ages over 10 it was slightly higher than in the earlier 
period. The critical age is evidently 0-5 ; but to bring out the 
real facts in connection with this age-period, it would be necessary 
to classify the deatlis according as they occurred in vaccinated or 
unvaccinated children, which the above figures do not attempt. 
Furtliermore, if we trace the period of compulsorily enforced 
vaccination from 1872, it is obvious that only those born after 
1871 can be affected by this compulsion. Hence not only does 
the age-period 0-5 require to be further subdivided, but the 
deaths at ages over 5 are outside the scope of compulsory vacci- 
nation. These are the ages which show the greatest increase of 
small-pox, during 1871-75. The significance of these facts will 
be made clearer by a study of Figs. 30 and 31. 

Small-pox in other Countries. In Sweden complete records 
of mortality from 1774 onwards are available. It is impracticable 
to reproduce these in full here,* but the main points may be 
gathered from the following figures : — 

SwEBEN. — (a) Before vaccinafioji (1774-1800) highest death- 
rate from small-pox was 7227 per million inhabitants in 1779; 
lowest Avas 311 in 1786; average of 27 years = 2008. 

{h) Permissive vaccination (1801-1815): highest death-rate, 
2570 in 1801 ; lowest, 121 in 1814; average of 15 years = 631. 

(c) Compulsory vaccination (1816-1885) : highest death-rate, 
935 in 1874; lowest, 0-5 in 1846; average of 70 years = 173. 

In Prussia the death-rates from small-pox for the period 1816- 
82 were as follows : — 

Vaccination in quinquennial groups, and then dividing by 5, instead of by 
the more accurate method of adding together separately the deaths and the 
population for each five years, and then calculating the death-rate. The error 
is a very small one. 

* See Vaccination aiid Small-pox. By Dr. E. J. Edwardes. Churchill, 
1892. 



214 VITAL STATISTICS. 

Prussia. — Death-rates ]3er 100,000 living. 

1816-30.— 45, 27, 29, 20, 10, 17, 20, 19, 14, 15, 14, 25, 19, 

19, 24. 
1831-50.— 11, 30, 60, 48, 27, 18, 15, 16, 14, 16, 14, 22, 28, 

27, 15, 15, 9, 13, 10, 15. 
1851-70.— 12, 18, 39, 43, 9, 7, 13, 26, 19, 18, 30, 21, 33, 46, 

43, 62, 43, 18, 19, 17. 
1871-72.-243, 262. 
. 1873-74.— 35, 9. 

Revaccination of general population in school-age made com- 
pulsory in 1874. 

1875-82.-3-6, 3-1, 0-3, 07, 1-2, 2-9, 3-6, 3-6. 
1883-86.— 4-0, 1-5, 1-4, 0-5. 

The following figures for Austria are important, as apart from 
the enforcement of tine vaccination law of 1874 in Prussia, all 
other conditions appear to be tlie same in the two countries. (See 
Dr. A. F. Hopldrk's evidence before the Royal Commission.) 

Austria. — Death-rates per 100,000 living. 

1842-44.— 20, 16, 13. 

1845-46. — Data are wanting. 

1847-71.-14, 18, 21, 15, 26, 25, 51, 59, 62, 31, 36, 56, 44, 

23, 22, 31, 53, 84, 45, 36, 47, 33, 35, 30, 39. 
1872-74.— 189, 323, 178. 
1875-81.— 57, 39, 53, 60, 50, 64, 82. 

It Avould be easy to multiply instances of comparisons between 
comparatively well-vaccinated and comparatively badly-vaccinated 
communities, but the following figures dealing with the ejjidemic 
years centring about the year 1871 must suffice.* 

Small-pox. Deaths per inillion living in the two toorst years 
of the epidemic 1870-74 (Korosi). Comparatively badly-vacci- 
nated countries: Prussia (1871-2), 5060; Holland (1870-2), 
5490; Austria (1872-4), 6180. Comparatively well-vaccinated 
countries: Scotland (1871-2), 1470; England (1871-2), 1830. 

Further instances may be obtained in the evidence given before 
the Eoyal Commission on "Vaccination. 

* From KoEosi's Kritik der Vaccinations statistik und neite Beitrdge zur 
Frage des Impfschulzes. Berlin, 1890. 



leatli-ratos 3000 
ler Million 
f Births. 



2000 



1000 



Ofatli-rato 1 000 
per M illion 
of ropula- 
tion. 




Fio. 30.— Death-rates from Small-pox, in England and Wales, according to Age (1847-94). 
(a) Death-rates from Small-pox and Chicken-pox under One Year of At'C per Million Births, (h) Deaths from Small- 
pox at all Ages under Five per Million living at these Ages, (o) Uitto, Aged 5-10, (d) Ditto, Aged 10-15. 
(f) Ditto, Aged 15-25. (/) Ditto, Aged 25-45, (g) Ditto, Aged 45 and over. 



216 VITAL STATISTICS. 

Age -incidence of Small -pox Mortality. Fig. 29 shows the 
variations in the death-rate from small-pox at all ages together 
since 1847. In Fig. 30 the same facts are shown for different 
age-periods, and it is particularly instructive to note the differences 
in the decline of the small-pox death-rate at different ages. 

In the uppermost curve (a) of Fig. 30 the deaths from small- 
pox and chicken-pox together, under one year of age, are plotted 
out as a rate per 1000 births in each year.* The two have 
been stated together because of the alleged confusion between 
these two diseases in the returns for earlier years. The inclusion 
of chicken-pox probably does not materially affect the height or 
fluctuations of the curve, but Dr. McVail's remarks, quoted below, 
should be noted. 

The statistics embodied in tlie uppermost curve are derived from Dr. 
Ogle's table on p. 646 of the Sixth Report of the Royal Commission on 
Vaccination ; those in the lower curves from the table on p. 155 of the 
Final Report of the Royal Commission on Vaccination. 

Subject to intercurrent epidemics, this curve shoAvs a steady 
decline of small-pox mortality in infants, interrupted by the 
epidemic of small-pox in 1870-71, an interruption which we have 
already noted is shared to a much greater extent by every other 
age of life. 

At all ages under 5, and at ages between 5 and 10 (Fig. 30, 
h and c), there has been a similar and equally marked decline 
of mortality from small-pox, while at the higher ages there is 
comparatively little alteration. 

Dr. McVail points out, however, that the number of deaths 
registered as being due to chicken-pox in years in which small- 
pox is not ejjidemic, may be nearly as great as the small-pox 
deaths. In epidemic years it might reasonably be expected 
that if these deaths were really due to small-pox they Avould 
probably be greater in number than in non- epidemic years, 
which is not the case. The above lumping together of deaths 
from small-pox and from chicken-pox would therefore lead to 
some error as to age-incidence of small-pox deaths in infancy, when 
these are stated as a percentage of total small -pox deaths at 
all ages. Hence in Fig. 31 (a), the infantile small-pox deaths 
do not include chicken-pox deaths. The error is so small, when 

* The deaths under one year of age from small-pox and from chicken- 
pox are classed together in the above diagram, on the supposition that a 
considerable pro}iortion of the deaths registered as due to chickeu-piox were 
really due to small-pox. 




a a-5 




pq .5 



SMALL-POX AKD VACCINATION. 217 

the infantile deatlis are stated in terms of the infantile population, 
that Dr. Ogle's figures have been given in Fig. 30 (a) in order 
to avoid laborious re-calculations. If the subject were left at 
this point, a most important lesson would escape attention. Tliis 
can only be brought out by considering wliat proportion of the 
total deaths from small-pox have occurred at diiferent ages in 
successive years. Tliis is shown in Fig. 31. 

The statistics embodied in Fig. 31 are derived from the table on p. 154 
of the Final Report of the Royal Commission on Vaccination. 

Fig. 31 brings out in a remarkable manner the altered age- 
incidence of small-pox mortality. Thus, in the uppermost curve 
(a) of this figure, Ave note that small-pox mortality in infancy, 
prior to 1870, nearly always formed 20 per cent, or more of the 
total mortality from this disease ; between 1870 and 1890 the 
small-pox mortality at this age did not greatly exceed 10 per cent, 
of the total, but since 1890 it has again begun to form an in- 
creasing proportion of the mortality at all ages. At ages 1-5 
(Fig. 31, h), the change is eveir more remarkable. Before 1870 
the small-pox deaths between 1 and 5 years of age nearly always 
exceeded 30 per cent, of the total; since 1870 they have varied 
between 5 and 14 per cent, of the total; while since 1890 they 
have formed, as under 1 year of age, an increasing proportion of 
the total small-pox deaths. At ages 5-10 (Fig. 31, c), a similar 
but less extensive alteration has occurred. Between 10 and 15 
(Fig. 31, d) there is some proportional increase. At ages 15-25 
(Fig. 31, e), the increase since 1870 is very marked, while at ages 
over 25 the same phenomenon is visible. 

How is this alteration of age-incidence of small-pox mortality 
to be explained 1 It is plain that some influence or influences 
have been at Avork (a) making small-pox much less fatal in 
England and Wales ; (6) that the reduction in tile death-rate 
from small-j^ox has l^een greatest under ten years of age ; (c) that 
of the reduced death-rate from small-pox which has occurred in 
recent years, a much higher proportion has fallen in adult life, 
so much so that the age-incidence of small-pox mortality may be 
described as almost exactly inverted ; {d) that in the last few 
years the curves show a tendency for smaU-pox to revert towards 
its original type as a disease chiefly fatal among children. 

The explanations given of this altered age-incidence are — 

(1) That it has been effected by the more or less general 
vaccination of the community. 



218 VITAL STATISTICS. 

(2) That it is caused by sanitary improvements, which operate 
more effectually upon young children than upon others. 

(3) That it is explicable by the fact that epidemics of small- 
pox now occur at longer intervals than formerly Avhen measures 
of isolation were unknown, and when inoculation was generally 
practised. 

(1) If the supposition that the great fall in small-pox mortality 
is due to vaccination is correct, why has the mortality from 
small-pox among those beyond 15 years of age not shared in this 
decrease 1 To begin with, the protection afforded by vaccination 
is less perfect than that afforded by a previous attack of small- 
pox; and in the next place it is less permanent. Its protective 
influence steadily diminishes, Avhile that of an attack of small-pox 
remains almost unaltered. Starting with these facts, the change 
in the age-incidence of small-pox is explained as follows : — 

Before the introduction of vaccination but few persons escaped 
having small-pox at some period of their lives, and the great 
majority had it Avhen young. Of these a large proportion died, 
making the small-pox mortality for the early age-periods high ; 
but those who survived, forming a large projjortion of the popula- 
tion at the later age-periods, and being permanently protected by 
an attack of small-pox, made the small-pox death-rate of the later 
ages a low one. With vaccination the susceptibility of young and 
old was altered, and in large measure inverted, Avith a corresponding 
effect on the small-pox mortality at different ages. 

The changes in the age-incidence of small-pox are so great as 
entirely to preclude any possibility of referring them to errors of 
registration or fluctuations due to chance. The most natural and 
probable explanation of them is that vaccination confers an im- 
munity from small-pox in the earlier years of life, which, however, 
is less complete and permanent than the immunity conferred by 
an attack of small-pox, thus explaining the fact that the higher 
ages have not shared in the improvement, and at the same time 
indicating the necessity for re- vaccination at the age of puberty. 

(2) "We must consider the hypothesis which maintains that the 
decline in small-pox mortality is due, not to vaccination, but to 
general improvement in the sanitary condition of the community. 
To begin with, no scrap of evidence is forthcoming, which shows 
any connection between bad drainage or other sanitary defects and 
small-pox. In this respect it is like measles and whooping-cough, 
which remain as prevalent as formerly, despite the immense 
strides which have been made in sanitary improvements. In 



SMALL-rOX AND VACCINATION. 219 

denying any connection between insanitation and small-pox, an 
exception must be made in respect of overcrowding. Like other 
infectious diseases, small-pox is most easily spread when, the most 
frequent opportunities exist for personal intercourse. It is therefore 
most often met with, and greater in amount, in busy centres of 
population than in scattered rural districts. The most noteworthy 
feature of the last forty years has been the ra^^idly increasing 
urbanization of the population, and the immense extension of 
travelling conveniences. And yet, notwithstanding the increase of 
these adverse influences, the small-pox death-rate has rapidly 
declined. 

(3) Dr. McVail, in his evidence before the Eoyal Commission, 
pointed out that the age-incidence of deaths from small-pox 
would vary according to the interval between epidemics. Thus, 
in Kilmarnock and Geneva, during last century epidemics came 
every four or five years, and nine-tenths of the deaths from small- 
pox occurred in children under 5 years of age. In Boston, U.S.A., 
epidemics came about every twelve years, and the average at death 
would therefore be higher than the above. For the unvaccinated 
the periodicity of the disease governs the age-incidence, with the 
limitation to be immediately noted ; for tJie vaccinated this is not 
so. The limitation referred to is that furnished by the fact that 
the protected state of the vaccinated diminishes the chances of 
infection, even for the unvaccinated, and therefore diminishes the 
mimber of epidemics. Hence the age-incidence of deaths from 
small-jDox among the unvaccinated will be higher in a generally 
vaccinated than in a generally unvaccinated community. Thus 
in the years 1881-87, of 3099 unvaccinated deaths from small- 
pox only 39 per cent, were under 5 years of age, as compared Avitli 
about 80 per cent, in the last century (McVail). At the same 
time, of one hundred vaccinated deaths from small-pox only nine 
were under 5 years of age. 

As regards inoculation, it is only necessary to examine Figure 29, 
noting at the same time the historical fact that inoculation of 
small-pox was made illegal in the year 1840.* 

As regards isolation of small-pox patients, this has undoubtedly 
contributed to minimize outbreaks ; such isolation has only been 

* The Report of the Royal Commission on Vaccination (p. 17) states, "it 
seems probable that inoculation did not tend to increase the prevalence of 
sniall-pox. In London, during]; the eighteenth century, little or no inoculation 
was practised until after 1740, but it rapidly increased after that date, and 
yet small-pox showed as marked an increase in the first half of the century 
as in the second. 



220 



VITAL STATISTICS. 



systematically applied in recent years, and in a limited number of 
districts. It does not, furthermore, explain why in recent years 
there is a distinct tendency for small-pox to become again, to a 
greater extent, a disease of early life. 

The recent neglect of vaccination in large communities is at 
least a feasible explanation of this latter fact : and if we study 
Figures 30 and 31 in view of the facts that— 

(1) From 1847-53 inclusive gratuitous vaccination Avas provided, 

but recourse to it was purely optional ; 

(2) From 18.54-71 vaccination was obligatory, but there were no 

effectual means to enforce the obligation thus instituted ; 

(3) From 1871 onwards. Boards of Guardians were obliged to 

appoint public vaccination officers in each district, and 
vaccination was more effectively enforced ; * 

(4) In more recent years, especially since 1890, there has been 

increasing neglect of vaccination ; 
the conviction is forced ujDon the mind that the reduction in 
small-pox mortality, and the alteration in age-incidence of the 
residual mortality, are related to each other as cause and effect. 

Altered Age-incidence of other Diseases. An attempt was 
made in the Dissent of Dr. Collins and Mr. Pictonf to show that 
other diseases show changes in age-incidence analogous to those in 
small-pox. 

Typhus and Typhoid Fever have been instanced. The difficulties 
of diagnosis render this comparison largely nugatory. It is well 
known that formerly many deaths among the very young were 
entered as caused by "fever," which would now be returned 
under their j^roper headings in connection with cerebral and 
respiratory affections, and especially with tuberculosis (pp. 200 
and 239). The percentages of deaths under 5 to deaths at all 
ages for four successive quinquennia are as follows : — 





1S71-75. 


1S76-SO. 


1881-85. 


1886-90. 


Typhus 
Typhoid . 


6-4 
17-4 


6-1 
16-0 


3-5 
9-3 


3-4 

7-5 



* It is probable that the law of 1871 made more difference in the vaccina- 
tion age than in the number vaccinated. It caused vaccination in the early 
months of life to be much more regularly adhered to (McVail). 

t Op. cit., p. 184 ct seq. 



SMALL-rOX AND VACCINATION. 



221 



It will lie noted tliat a sudden change in age-incidence occurred 
in 1881-85, and that since that time no further great change has 
occurred. Compare this with the continuing alteration in age- 
incidence shown in Fig. 31. It must he noted furthermore that 
fatal small-pox, unlike "fever," is not a disease in which difficulties 
of diagnosis can occur, except with the greatest rarity. The 
first three columns of the following table are taken from pp. 
cxii.-cxiii. of the Supplement to the Forty-fifth Annual Report 
of the Reriistrar-General. The last column has been calculated 
by the author. 

The death-rate from each cause is taken as unity, and then the 
death-rate at ages under 5 is stated proportionately to this. 

Proportional Mortality under 5 years of Age. 
(Mortality at all Agos = l.) 





1851-60. 


1861-70. 


1S71-S0. 


1881-90. 


From all Causes 


3-0 


3-0 


2-9 


3-0 


,, Measles .... 


6-8 


6-8 


6-8 


7-1 


, , Scarlet Fever . 


4-7 


4-7 


4-8 


5-0 


,, Diphtheria 


4-0 


4-1 


3-9 


4-2 


,, AVhoo] ting-cough . 


7-2 


7-2 


7-1 


7-5 


,, Diarrhoea 


4-9 


^■& 


6-1 


6-4 


,, Fevers (including typhus, 










typhoid, and ill-detiued) 


1-5 


1-4 


1-3 


0-8 


,, Small-pox 


4-7 


4-0 


2-2 


1-8 



In most of the above diseases, the proportion of deaths under 
5 has remained stationary or slightly increased, with the exception 
of " fever " (a doubtful whole, in which immense difficulties of 
diagnosis are involved), the proportion of which under 5 has 
declined from 1*5 to 0*8 ; and small-pox (a well-marked and easily 
recognizable disease in its fatal form), in which the proportion has 
declined from 4*7 to 1'8. 

It must be remembered that the comparison in the above tables 
is between periods of less and of more vaccination, and not 
between periods of vaccination and no vaccination. This makes 
comparison between small-pox reduction and " fever " reduction 
decidedly unfair. The causes of reduction of typhus and typhoid 
fever are recent causes, and almost their wliole effect is seen in 
recent years ; whereas small-pox had already shrunk from a giant 
to a dwarf before the years of the above comparison. 



222 



VITAL STATISTICS. 



Influenza has also been instanced, reference being made by Dr. 
Collins and Mr. Picton to the Fifty-fourth Report of the Registrar- 
General, in which he states that "the epidemic of 1890-91 was 
distinguished from the equally fatal epidemic of 1847-8 by the 
greater comparative severity with which it attacked persons of 
middle age." 

This comparison, only embodying two years of the recent 
epidemic of influenza, cannot be regarded as trustworthy. The 
question of diagnosis arises as in the case of "fever." In influenza 
there is no exanthem, and it is highly probable that in the two 
epidemics the proportion of cases in which the primary cause of 
death — influenza — or only the secondary cause, such as pneumonia, 
etc., was inserted in the death-certificate would vary considerably. 
Taking, however, the death-rates as they appear in Table G, p. xx. 
of the above report, I have calculated the percentage of total deaths 
from influenza at all ages which have occurred at each age-period, 
the result being shown in the following table : — 



Percentage of Total Deaths prom Influenza at all Ages 

OCCURRING AT EACH AgE-PERIOD. 



Age-period. 


1S47-4S. 


1890-91. 


Under I 

5- 
10- 
15- 
20- 
25- 
35- 
45-" 
55- 
65- 
75- 








3-3 

0-4 

0-2 

0-2 

0-4 

0-6 

1-3 

3-8 

11-2 

25-8 

52-8 


2-3 

0-4 

0-3 

0-8 

1-5 

2-7 

4-6 

8.4 

15-4 

26-0 

. 37-6 




100-0 


100-0 



A comparison of this table with the results indicated in Fig. 31, 
shows that the attempt to prove any analogy between the two is 
entirely futile. 

Local Variations of Age-incidence of Small-pox. The report 
of the Eoyal Commission embodies a series of facts on this point, 
which are summarized in Fis:. 32. 




CO t--. ^ 



1^ CO 



(N O 

O r-l 






o Q 






224 YITAL STATISTICS 

The relative proportion of deaths from small-pox under 10 
years of age to total deaths from small-pox at all ages, varied in 
recent epidemics of this disease which were specially investigated 
on behalf of the Commission, from 22*5 in Warrington to 66 "6 
per cent, in Leicester. The relative proportion of cases under 
10 years of age varied from 9 "8 per cent, of the total number at 
all ages in Warrington to 35 "7 per cent, in Gloucester. In con- 
junction with these variations of age-incidence of small-pox we 
have the facts that in Warrington and Sheffield the percentage of 
the population unvaccinated was very small. In the ten years 
1883-92 the returns for the union of Warrington (which includes 
the borough) show that 4 '8 per cent, of the births were not 
accounted for. In London, in 1883, the percentage of births left 
unaccounted for was 6*5, gradually increasing to 16 "4 per cent, in 
1891. In Dewsbury the number not accounted for increased from 
12-6 per cent, in 1882 to 37*7 per cent, in 1892. In Leicester the 
percentage unaccounted for increased from 43"8 in 1883 to 80*1 
in 1892 ; in Gloucester from 10-6 in 1885 to 85*1 in 1894. 

The Royal Commission's report lays stress on the facts briefly 
summarized above, pointing out that they are not open to the 
same chance of error as is involved in a comparison of the mortality 
among persons said to be vaccinated or unvaccinated. 

It is contended on the other side that the proportion of attacks 
occurring among children will depend upon the incidence of the 
infection. Thus "in Warrington the small-pox Avas mainly spread 
in forges near the hospital, and there were 596 sufferers over 10 
to 65 children under 10. In Leicester, on the other hand, children 
were specially attacked owing to the proximity of the small-pox 
hospital to the scarlet fever wards." (It should be noted, however, 
that in the percentage of deaths in Leicester under 10, three deaths 
occurring in the scarlet fever wards have been omitted, thus 
reducing the proportion from 71 "4 to 66-6.) This contention 
might be accepted if, on investigation, it were found that the 
outbreak was confined to the particular section of the population 
among which it began. As the Leicester outbreak was speedily 
stamped out, such an assertion may be partially true for its small- 
pox in 1892-3. It is absurd, however, to assume that this explan- 
ation carries any weight in an instance like Gloucester, whose 
small-pox epidemic only ceased when all the susceptible persons 
in the city had been attacked. Furthermore, the facts that in 
Warrington large ironworks were selected for severe attack by 
small-pox, and in Gloucester one or two elementary schools suffered 



SMALL:POX AND VACCINATION. 225 

severely, is evidence of the value of primary vaccination, which 
was enforced in Warrington and not in Gloucester. In Leicester 
small-pox attacked the scarlet fever hospital, the scarlatinal occu- 
pants of which were sent home, where scarlet fever became widely 
epidemic. 

It is further contended * that the age-incideiice argument is full 
of danger, as it ignores the " true fatality results." These, it is 
asserted, can be tested by the Commissioners' own doctrine. This 
doctrine "implies that neglect of vaccination increases not only 
the liability to attack from small-pox, but the liability to severe 
and to fatal attack ..." 

This argument may be accepted as valid, and applied to the 
small-pox statistics of the six above towns. 

Fatality of Small-pox. In dealing with such fatality statistics 
it must be borne in mind that unless the number of facts on which 
the percentage is based is substantial, the percentage can carry 
little or no weight. The most serious errors made by physicians 
in concluding, for instance, that a given drug is particularly 
efficacious, have owed their origin either (a) to the fact that the 
number of cases treated was very small (on this point see alsb 
pp. 185 and 323), or {h) no allowance was made for age and other 
causes of variation in contrasting different therapeutical methods. 

It is further to be remembered that small-pox, like all other 
infectious diseases, varies considerably in virulence, and there- 
fore in fatality in different epidemics. Thus in the six towns 
already mentioned, it is probable that persons over 20 years of 
age, are in about the same condition as regards vaccination ; but 
the fatality among these Avas : Gloucester, 14*0 ; Sheffield (to 
date of census), 10 "9; Warrington, 10 3; Dewsbury, 8'0; London, 
7'0 ; and Leices,ter, 2-2 per cent. 

The epidemic of small-pox in England and in other countries 
in 1870-72, probably OAved its origin, in part at least, to the fact 
that the contagium of small-pox acquired at that time increased 
infectivity, owing to conditions — either biological or cosmical — of 
which we are at present ignorant. 

It is asserted that the classification into vaccinated and un- 
vaccinated groups cannot be relied upon as accurate. Every care 
has however been taken in obtaining accurate statistics for the 
six above towns, and it cannot reasonably be maintained that 

* See pp. 10-15 of Mr. raiil's pamplilet. 



226 



VITAL STATISTICS. 



transference from one group to the other has occurred on a scale 
which would materially alter the broad result. 

In the six towns together, 2321 unvaccinated persons were 
attacked, of whom 35-4 per cent, died (Fig. 33). 

Among the vaccinated persons at all ages who were attacked, 
8744 or 5*2 per cent. died. 

Among the unvaccinated, 1449 attacks were at ages under 10, 
Avith a fatality of 36 '0 per cent.; 870 were over 10, with a fatality 
of 34*3 per cent. Among the vaccinated, 589 attacks were at 
ages under 10, with a fatality of 2-7 per cent. ; 8131 attacks were 
at ages over 10, with a fatality of 5*4 per cent. 



At all Ages, 



Under 10. 



Over 10. 



Unvaccinated 




Vaccinated 



Fig. 33. 

Percentage Fatality (Case Mortality) in Six Towns among Unvaccinated and 
Vaccinated under 10 and over 10 years of Age. 

Note. — 30-3 in the above diagram should be 36'0, and 2-3 should be 2'7, thus in- 
creasing the contrast between vaccinated and unvaccinated under 10 years of age. 



In the folloAving table the detailed facts for each of six 
towns, as given on pp. 55-58 of the Commissioners' report, 
are summarized : — 



SMALL-POX AND VACCINATION. 



227 











O 


u 


tj 
































JS 


£3 
O 


1 

Q 


■£ 
^ 


>3 


3 


Vaccinated cases under 10 . 


353 


110 


44 


33 


2 


26 


Fatality per cent. 


1-7 


0-0 


2-2 


6-0 


0-0 


3-8 


Unvaccinated casesunder 10 


288 


228 


174 


32 


107 


680 


Fatality per cent. 


43-9 


26-7 


32-1 


67-5 


14-0 


41-0 


Vaccinated cases over 10 . 


3774 


1643 


577 


560 


197 


1185 


Fatality per cent. 


5-1 


2-3 


2-6 


6-4 


1-0 


10-0 


Unvaccinated cases over 10 


322 


181 


192 


36 


51 


88 


Fatality per cent. 


54-2 


20-9 


18-7 


33-3 


7-8 


39-7 



* Ui) to the date of Dr. Barry's census. 

If the preceding figures are approximately true, even though 
a very liberal margin is alloAved for alleged but unproved mistakes, 
it is clear that vaccination is followed by an immense improvement 
in the prospect of recovering from attack of small-pox. 

Mr. Paul, in the pamphlet already mentioned, makes what he 
describes as a test contrast between Gloucester and Leicester. 
The argument of the Commissioners is, he states, " that no 
cause apart from vaccination can adequately account for the 
great variation in the small-pox fatality among the children of 
the six towns. AVhat is the fact? That the widest variation 
of all is observed where something other than vaccination must 
account for it ; because there was practically no vaccination in 
either case. These are the facts : — 





Unvaccinated. 


Died. 


Gloucester Children . 
Leicester Children 


96-31 
98-16 


39-66 
13-76" 



The error in the above table consists in lumping vaccinated 
and unvaccinated children together. The table on p. 226 shows 
that among the two vaccinated children in Leicester who were 
attacked, no deaths occurred, Avhile of the 107 unvaccinated 
children, 14 per cent. died. Similarly in C41oucester, the fatality 



228 ; VITAL STATISTICS. 

among 26 vaccinated children was 3"8 per cent. ; among 680 
unvaccinated children^ 41 "0 per cent. JN'o supposition about 
superior social status among the vaccinated will cover such 
differences as are here displayed. True, the fatality in both 
groups ■ was much lower in Leicester than in Gloucester ; hut 
the difference hetiveen the fatality in vaccinated and unvaccinated 
was greater in Leicester, both at ages under and over 10, than in 
Gloucester. 

Attack-rate among Vaccinated and tFnvaccinated. Fig. 34, 
embodying the figures given on p. 65 of the report of the Royal 
Commission, shows the greater liability to attack by small-pox of 
the unvaccinated, and brings out the fact that the protection 
against attack imparted by vaccination decreases with advancing 
age. It is evident that the liability to attack depends primarily 
on contact with or proximity to sources of infection. Fig. 34 
gives the percentage of attacks occurring among persons living in 
infected houses, classified according to vaccination and according to 
age under and over 10. The facts illustrated in Fig. 34 are based 
on all the houses from which the required information could be 
obtained. Their proportion to the total number of infected 
houses varied in different towns. Thus the information was avail- 
able at Warrington for 437 out of 457 houses invaded, at DeAVS- 
bury for 544 out of 648 houses invaded, at Leicester for all 
invaded houses, at Gloucester for 899 out of a total of 1097 
invaded houses. 

Had sjDace allowed, I had proposed to discuss the relationship 
betAveen severity of attack of small-pox and vaccination, differ- 
entiating betAveen the different qualities of vaccination : also to 
summarize the experience of the army and navy, and of other 
countries. For details on these and other points, the reader is 
referred to the Royal Commission's report. It has ahvays 
appeared to me that the most convincing argument is that derived 
from the almost complete immunity from small-pox enjoyed by 
re-vaccinated nurses in small-pox hospitals. Thus, in the ex- 
perience of the staff of the Metropolitan Asylums Board Hospitals, 
in the six years 1890-95, out of a staff varying from 1160 to 2514, 
the number who contracted scarlet fever, diphtheria, or typhoid 
fever during each year varied from 4'0 to 7*3 per cent, of the total 
staff; while out of a staff varying from 64 to 320, the percentage 
attacked by small-pox Avas nil, except in 1892, when it was 1'4, 
and in 1893 Avhen it Avas 1'9. 



Vaccinated. Unvaccinated. Vaccinated. Unvaccinated. 



Wanirii'ton 




Du\vsl)ur 



Cloucfster 



Fio. 34, 

Rate of Attack per 100 Persons living in hoiises invaded by Sniall-pox among 
Vaccinated and Unvaccinated under 10 and over 10 years of Age. 



230 VITAL STATISTICS. 

The advantages of vaccination have been summarized as follows 
by the Eoyal Commission : — 

"(1) That it diminishes the liability to be attacked by the disease. 

" (2) That it modifies the character of the disease, and renders it (a) 
less fatal, and {b) of a milder or less severe type. 

" (3) That the protection it affords against attacks of the disease is 
greatest during the years immediately succeeding the operation of 
vaccination. It is impossible to fix with precision the length of this 
period of highest protection. Though not in all cases the same, if a 
period is to be fixed, it might, we think, fairly be said to cover in 
general a period of nine or ten years. 

" (4) That after the lapse of the period of highest protective potency, 
the efficacy of vaccination to protect against attack rapidly diminishes, 
but that it is still considerable in the next quinquennium, and possibly 
never altogether ceases. 

" (5) That its power to modify the character of the disease is also 
greatest in the period in which its power to protect from attack is 
greatest, but that its poAver thus to modify the disease does not diminish 
as rapidly as its protective influence against attacks, and its efficacy 
during the later periods of life to modify the disease is still very 
considerable. 

" (6) That re-vaccination restores the protection M'hich lapse of time 
has diminished, but the evidence shows that this protection again 
diminishes, and that, to ensure the highest degree of protection which 
vaccination can give, the operation should be at intervals repeated. 

" (7) That the beneficial effects of vaccination are most experienced 
by those in whose case it has been most thorough. We think it may 
fairly be concluded that where the vaccine matter is inserted in three 
or four places, it is more effectual than when introduced into one 
or two places only— and that if -the vaccination marks are of an area 
of half a square inch, they indicate a better state of protection than, if 
their area be at all considerably below this." 



CHAPTEE XX. 
MORTALITY FROM CERTAIN INFECTIVE DISEASES. 

PUERPERAL FEVER. The last edition of the nomenclature 
of the Royal College of Physicians states : — 

"The term 'Puerperal fever' should no longer he used. Pyemia, 
Septicaemia, or Saprsemia, occurring in puerperal women should be 
described as ' Puerperal pytemia,' ' Septica3mia,' or ' Saprtemia ' respec- 
tively. The other conditions included under the term ' Puerperal 
fever' should be returned under Afl'ections consec^uent on Parturition, 
the word ' Puerjjeral ' being in all cases prefixed to the word denoting 
the local process." 

It is doubtful, however, whether such exact definition is always 
possible. Most cases of puerperal fever are undoubtedly septic 
in origin ; but it would often be difficult to go farther than this 
in stating their true j^athological character. The advice given in 
the books of forms of certificates of death should, however, 
always be followed: "that whenever childbirth has occurred 
within one month before death, this fact should be registered in 
connection with the cause of death." This has been to a large 
extent neglected in the past by medical practitioners, and during 
the ten years 1881-90 letters sent out from the General Register 
office have resulted in over 1000 deaths being transferred to 
puerperal fever out of about 4000 deaths, the certified cause of 
which was "Peritonitis," occurring in women of child-bearing 
age. Again, of more than 3000 deaths returned as from pysemia, 
blood-poisoning, etc., about 700 were ascertained to have been 
due to puerperal causes, and nearly half of 244 deaths ascribed in 
the certificates to metritis required to be similarly transferred. 

PuerjDeral fever being confined to parturient women, it is prefer- 
able to calculate the death-rate from it in terms of the number of 
births rather than of the number of the entire population, as in 
the following table : — 

231 



232 



VITAL STATISTICS. 



Annual Number of Deaths of Mothers to 1000 Children 
Born Alive. 



Number of Deaths. 


o 

2 


o 
J;- 


o 
1 

00 


O 

1 


o 


Puerperal Fever and other 
accidents of Childbii'th 
Pnerjjeral Fever 
Accidents of Childbirth . 


4-8 
1-5 
3-3 


47 
1-5 
3-1 


4-7 
2-1 
2-7 


4-7 
2-6 
2-2 


2-5 



Thus in 1881-90 to every 1000 children born alive, 4-73 death 
of mothers occurred, or one maternal death to 211 live-born 
children. 

It should be remembered that the number of cliild-hearings is 
not equivalent to the number of births. The birtlis indicate the 
children born alive. Some other children are stillborn, and some 
are multiple at birth. Excluding the still-births, the number of 
child-bearings is obtained by reducing the number of births in 
about the proportion of 1 to 0*9902. 

The following table [Supplemeiit to the Registrar-GeneraVs Fifty- 
fiftli Annual Report, part i. p. ex.) shows the incidence of puerperal 
mortality at different ages. 

Death-rate per Million Females living at each Age-period 
FROM Puerperal Fever and Childbirth. 



1861-70 


All Ages. 


10- 


15- 


20- 


25- 


35- 


45- 


55- 


321 





161 


633 


921 


888 


60 


_ 


1871-80 


325 


1 


167 


678 


946 


886 


53 


— 


1881-90 


297 





129 


601 


888 


802 


43 






The preceding table is not free from fallacies. The diiferences 
shown between the rates at each age-period may be caused solely 
by alterations in the risks of childbirth or by alterations in the 
birth-rate of the population at the same age-period. For accurate 
purposes what is required is a statement of the number of births 
classified according to the age of the mother, distinguishing between 
the births occurring within and without matrimony. 

There is the further fallacy connected with average death-rates 
for series of years. This is brought out in the following curve, 



O'-' ** w i*^ u"35 M 00 «o o 



O 3- ^ p 



'1850 







' — 1860 



^ — 1880 



1890 



234 VITAL STATISTICS. 

wliich shows the mortality from puerperal fever in England and 
Wales from 1847 to 1896, stated in proportion to the numher of 
births. 

The curve shows years of greater mortality from this disease, 
which make one suspect the possibility of its partaking in some 
respects of the character of an epidemic disease. Longstaff has 
shown that the chief increase in the death-rate from this disease, 
as well as that of erysipelas, occurs in years of deficient rainfall. 
Both Gresswell and Longstaff have shown that the yearly mortality 
from scarlet fever is also inversely to the amount of rainfall. I 
have shown a similar relationship between deficient rainfall and 
the epidemic prevalence of diphtheria * and of rheumatic fever.t 
Now the years since 1881 have been almost without exception 
years of deficient rainfall, and this protracted deficiency of rainfall 
has corresponded with a jDrotracted excess of puerperal fever, as 
well as of the diseases mentioned above. Another factor came into 
operation in 1881, and has been continued in subsequent years, 
viz., the sending out letters of inquiry from the General Register 
Office, as already indicated. It may, therefore, be that these two 
factors have produced an increase of registered mortality from 
puerperal fever, and that there has been no greater carelessness in 
precautions against sepsis on the part of accoucheurs or midwives, 
as the figures might at first sight indicate. If this supposition is 
correct, then with the next cycle of wet seasons puerjDeral mortality 
will again decline. It may decline beyond what may be described 
as the "normal" extent, if antiseptic precautions are rigidly prac- 
tised in connection with midwifery. 

A further subject of inquiry is the relationship of puerperal 
mortality to the primiparous or multiparous condition. No official 
English data are available on this point. Valuable information, 
both for the business of life insurance and for medical purposes, 
would be secured by making it obligatory to insert the ages of the 
parents of the children whose births are registered, and the position 
of the child in the family. (See p. 69.) 

Mr. T. A. Coghlan, government statistician for ISTew South 
Wales, gives some valuable information on these points, based 
on the 115,669 confinements and 813 deaths due to childbirth 
registered in New South Wales in the four years 1893-6. 

* Epidemic Diphtheria: a Research on the Origin and Spread of the 
Disease, 1898. 

+ See Mih'oy Lectures by the Author. Lancet, March 9th and 16th, 
1895. 



MORTALITY FROM INFECTIVE DISEASES. 235 



The births and deaths in childbirth being arranged according to 
the number of the confinements, show a probabihty of deatli in the 
first confinement of 0-0087, in the second 0-0066, in tlie fifth of 
0-0052, in the tenth of 0-0097, in the thirteenth of 0-0168. The 
risk attending the first liirtli is greater than that at any subse- 
quent one up to the ninth. The minimum risk appears to be at 
the fourth confinement, but the increase in the risk at subsequent 
confinements may be due to the increased age of the mother. 
When the first confinements are arranged according to the age 
of the motlier, it is seen that the rislc attendant upon a first 
birth is at a minimum at the twenty-second and twenty-third 
years, and after five years increases rather rapidly with age. 
The following table summarizes some of Mr. Coghlan's most im- 
jjortant results {Journ. Royal Statist. Soc, vol. Ixi. part iii.) : — 

Table showing for New South Wales, 1893-96, the unadjusted 
Death-rates per cent, op Childbed for Quinquennial Groups 
OP Ages. 



Age. 


Coghlan, New South Wales. 
Deaths of Childbed. 


Primiparte. 


Primiparse and Multipara 
combined. 


Married. 


Married. 


Unmarried. 


17-19 

20-24 

25-29 

30-34 

35-39 

40-44 


0-860 
0-634 
0-935 
1-507 
1389 
3-247 


0-726 
0-439 
0-508 
0-674 
0-855 
1-132 


1-199 
1-095 
0-748 
1-038 
0-189 
0-602 



From his adjusted figures INIr. Coghlan comes to the conclusion 
that " the risk of unmarried women in childbirth is at every age 
greater than for the married, the disproportion in the ratios being 
greatest at the lower ages." 

N.B. — j\Ir. Coghlan employs a graphic method of adjustment 
similar to that described on pp. 246 and 265. 

The local incidence of puerperal mortality for each county is 
given in the Sxcpplement to the Fifty-fifth Annical Report of tlie 
Registrar-General, p. Iii. The average number of deaths from 
puerperal fever and other accidents of childbirth per 1000 births 
in 1881-90 Avas 4*7 for England and AVales, varying from 6-7 in 



236 



VITAL STATISTICS. 



JSTortli Wales, 6-1 South Wales, and 5-5 Shropshire, Lancashire, 
and Cheshire, to 4-0 in Kent and Bedfordshire, 3-9 London, 3-7 
Suffolk, 3-5 Rutlandshire, and 3-3 in Huntingdonshire. A fallacy- 
lurks in average death-rates for a disease, such as puerperal fever, 
which is much more prevalent in certain years than in others. 
(See p. 232.) 

Tubercular Diseases. The two folloAving tables give the chief 
figures as to the mortality from these diseases in England. In 
the first table the corresponding data for diseases of the respiratory 
organs (other than phthisis) are given for comparison : — 

England and Wales : Mortality prom Phthisis, other Tuber- 
cular Diseases, and Diseases op Respiratory Organs per 
Million Persons Living at all Ages. 





1861-70. 


1871-80. 


lSSl-90. 


1891-95. 


1896. 


Phthisis 

Other Tiibei'cular Diseases 
Diseases of Respiratory System 


2475 

765 

3591 


2116 

747 
3899 


1724 

696 

3729 


1464 
660 

3747 


1307 

685 

3034 



In the following table the facts as to phthisis are classified 
according to age and sex : — 

Mortality from Phthisis in Groups op Years, 1861-96, per 
Million of each Sex Living at each Group op Ages. 





All 

Ages. 












1 








75 and 


Periods. 


0- 


5- 


10- 


15- 


20- 


25- 35- 

i 


45- 


55- 


65- 


up- 
wards. 


MALES. 


1851-60 . 


2579 


1329 


525 


763 


2399 


4052 


4031 


4004 


S830 


3331 


2389 


928 


1861-70 . 


2467 


990 


431 


605 


2190 


3883 


4094 


4166 


3861 


3297 


2024 


659 


1871-80 . 


2209 


783 


340 


481 


1675 


3092 


3699 


4120 


3860 


3195 


1924 


603 


1881-90 . 


1847 


553 


253 


342 


1287 


2333 


3024 


3562 


3488 


2916 


1816 


688 


1891-95 . 


1633 


467 


197 


260 


1076 


2026 


2548 


:i268 


3205 


26S7 


1572 


663 


1896 


1485 


392 


150 


203 


913 


1848 


2285 


3029 


3043 


2599 


1329 


512 










FEMALES. 




1851-60 . 


2774 


1281 


620 


1293 


3516 


42SS 


4575 i 4178 


3121 


2383 


16,S5 


716 


1861-70 . 


2483 


947 


477 


1045 


3112 


3967 


4378 


3900 


2850 


2065 


1239 


447 


1871-80 . 


2028 


750 


375 


846 


2397 


3140 


3543 


.S401 


2464 


1777 


1093 


407 


1881-90 . 


1609 


518 


327 


699 


1800 


2315 


2787 


2730 


2053 


15] 2 


974 


397 


] 891-95 . 


1303 


421 


260 


561 


1428 


1740 


2155 


2305 


1742 


1294 


800 


350 


1896 


1139 


349 


204 


454 


1183 


1562 


1874 


2090 


1543 


1170 


676 


375 



Death -HfiTES from PHTH/SIS in ENGLAND ^nd ^ WALES pK/OOOO /Mn^ , W38 - 1894- . 



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MORTALITY FROM INFECTIVE DISEASES. 237 

It thus appears that the death-rate per 1000 at all ages has 
declined from 2*58 for males and 2-77 for females to 148 for 
males and 1*14 for females. The accompanying diagram (Fig. 36) 
by Dr. Ransome {Lancet, July 11th, 1896) graphically represents 
the decline for a still longer period. Between 1838 and 1894 the 
phthisis death-rate had declined from over 3*8 to only 1"38 per 
1000 inhabitants. The line joining the highest and the lowest 
points of the curve (dotted lines) is approximately straight, and 
not a hyperbola, thus demonstrating, as pointed out by Dr. Venn, 
that the rate of diminution is an increasing one. The fall Avould 
have been more gradual had the percentage of diminution re- 
mained constant during the period under observation. 

From the year 18-51 to 1865 the phthisis death-rate was greater 
among females than among males, the difference between the two 
gradually diminishing. Since 1866 the phthisis-rate has been 
uniformly in excess among males, and increasingly so. 

The following table shows that while the decrease of mortality 
from phthisis among males has amounted to 37 per cent., that 
among females has been 53 per cent. 

In the same table I have calculated the percentage reduction at 
each age-group for the two sexes, the comparison being between 
the decennium 1851-60 and the quinquennium 1891-95. 

Percentage Eeduction of Phthisis Death-rate between 
1851-60 AND 1891-95. 





AU Ages. 


0- 


5- 


1 fl- 


15- 


20- 


25- 


So- 


45- 


.55- 


05- 


75 and 
upwards. 


Males 
Females 


37 
53 


65 
67 


63 

58 


ee 

57 


55 

59 


50 

59 


37 
53 


ls 
45 


16 

44 


19 
46 


34 
51 


39 
51 



The decline in phthisis mortality, it will be seen, is greater at 
nearly all ages in females than in males, the only exceptions being 
between 5 and 15 years of age. 

Another interesting point can be gathered from the tal)le on 
p. 236, and is more clearly brought out in the following table 
{Report of Royal Commission on Tuberculosis, Part ii., Appendix 
C, Dr. Tatham) :— 



238 



VITAL STATISTICS. 



Ages of Maximum Mortality from Phthisis. 

(The age-groups in heavy type have the maximum rates, the others 
being approximate.) 



Periods. 


Males. 


Females. 


1851-60 . 


20-25, 25-35, 35-45 


25-35 


1861-70 . 


25-35, 35-45 


25-35 


1871-80 . 


35-45 


25-35 


1881-85 . 


35-45 


25-35 


1886-90 . 


35-45, 45-55 


25-35, 35-45 


1891^95 . 


35-45, 45-55 


35-45 



The age of maximum phthisis mortahty has been postponed in 
both sexes. This may be ascribed to a greater saving of life at 
those ages formerly most liable to death from phthisis, or to a 
postponement of death in those who are attacked by the disease. 
Probably both causes are at work. 

The question arises as to hoAV far the reduction in registered 
mortality from phthisis is real, and how far it is due to more 
accurate diagnosis and certification of deaths. 

It is possible that, owing to more accurate statemen of causes 
of death, there has been considerable transference from phthisis to 
diseases (other than phthisis) of the respiratory organs. (See table, 
p. 236.) The term phthisis is now not so loosely used as formerly, 
when any chronic chest affection received this name. But that 
this is by no means a complete explanation of the decrease in 
phthisis, is evidenced by the fact that Avhile the mortality from 
phthisis has decreased at all age-groups, the mortality from respi- 
ratory diseases has only increased under 5 and over 75 years of 
age. Furthermore, the mortality from phthisis chiefly takes place 
betAveen the ages of 15-55 years, while that from respiratory 
diseases is very low during these years, and greatest at the 
extremes of life. 

In the following table I have calculated the reduction at each 
age-group between 1861-70 and 1896 for phthisis and for diseases 
of the respiratory system (exclusive of croup). In this instance 
1896 is taken rather than the quinquennium 1891-95, in order 
that the disturbing influence of influenza may be less operative. 



MORTALITY FROM INFECTIVE DISEASES. 239 



Percentage Reduction of Death-rate at each Age-group 
BETWEEN 1861-70 and 1896. 



Males 
Females 

Males 
Females 


All Ages. 


0- 


5- 


10- 


15- 


20- 


25- 


35- 


45- 


55- 


65- 


75 and 
upwards 


40 
52 


Phthisis. 




60 
63 


65 
57 


66 
37 


58 52 

62 61 

1 


44 
57 


27 21 
46 46 


21 
43 


44 22 

45 16 




Respiratoky Diseases. 


10 
11 


+ 5 5 
+ 4 11 


24 
32 


9 
36 


10 
36 


7 6 11 
28 21 21 


13 
21 


20 

20 


7 

+ 4 



Note.— All the figures represent decreases, except those preceded by +. 

In recent years there has been an increasing tendency to register 
deaths as due to "tuberculosis" or "general tuberculosis," which 
would formerly have been returned as phthisis. The result has 
been some exaggeration of the decline of the phthisis death-rate. 
The same cause has tended to keep up the death-rate from other 
tubercular diseases. Other causes have contributed to this effect. 
jNIany deaths now returned as tubercular meningitis would have 
appeared formerly as "fever" or "brain fever." It is probable 
that more cases of simple meningitis are returned as tubercular 
than the reverse. Again, many deaths formerly returned as 
marasmus, etc., are now ascribed to tabes mesenterica, and many 
more articular and other strumous diseases have their tubercular 
character plainly stated than in former years. There is strong 
reason for thinking that many deaths are now returned as tabes 
mesenterica where an autopsy would prove the absence of tuber- 
cular disease. 

The death-rate from tubercular meningitis (acute hydrocephalus) 
was 380 per million in 1880, falling to 233 in 1896. Tabes 
mesenterica (a time-honoured term, probably including certain 
other non-tubercular diseases besides tubercular aflections of the 
abdomen and its glands) declined from 403 in 1880 to_ 214 in 
1896; other forms of tuberculosis increased from 142 in 1880 
to 200 in 1896. In view of the preceding considerations, it is 
probable that the decline in all other tubercular affections than 
phthisis is greater than the official figures show. 



240 VITAL STATISTICS. 

The amount of mortality due to tubercular diseases still re- 
mains appallingly great. Thus, during 1896, 7 '6 per cent, of 
the total English mortality was caused by phthisis, and 11 '6 per 
cent, by all tubercular diseases together. Taking 15 to 55 as the 
most important working years of life, it is important to note that 
in the same year 26 '6 per cent, of the total deaths among males 
at these ages were caused by phthisis, and 28-9 per cent, by all 
tubercular diseases together. 

The local disfribufioii of phthisis mortality is given in the 
Suj^plement to tJie Fifty-fifth Aiimial Report of the Regutrar- 
General, part i. p. Ivii. et seq., the death-rates being calculated 
per standard million of population. Thus stated the phthisis 
death-rate in 1881-90 was 1724 for England and AVales, the 
highest being 2112 Korth Wales, 2095 Northumberland, 2003 
South Wales, and 2001 London; the lowest 1217 Worcestershire, 
1301 Herefordshire, and 1315 Leicestershire. In London, Hamp- 
shire, Sussex, Warwickshire, Surrey, Middlesex, and Worcester- 
shire the phthisis death-rate of males exceeded that of females 
by proportions varying from 27 to 55 per cent. In South Wales, 
Durham, Huntingdonshire, Lincolnshire, North Eiding of York- 
shire, JMonmouthshire, and Rutlandshire, on the other hand, the 
male rate was from 12 to 21 per cent. beloAv the female rate. 
The phthisis death-rate of London for 1881-90 is vitiated as 
regards both inclusion and exclusion by the lack of adjustment 
for deaths occurring in institutions within and without the 
metropolis. Such adjustments will be obtainable for more recent 
years. 



CHAPTER XXI. 



MORTALITY FROM CANCER AND CERTAIN 
OTHER CAUSES. 

CiAXCP]R. The registered mortality from cancer (including 
I under this name the various forms of malignant disease) has 
steadily increased, as shown in the following table : — 

Mortality from Cancer in England and Wales' per 
Million Living. 





1851-60. 


1861-70. 1871-80. 


1881-90. 


1891-95. 


1896. 


Males . . 195 
Females . . 434 
Persons . . 317 


242 312 
519 617 
384 468 


430 
739 
589 


to ' ' 


618 
901 
764 



Cancer is a disease of later adult life, as is shown by the 

following table, in which the death-rates per million living at each 
age-period in 1861-70 and in 1896 are compared: — 

Death-rates from Cancer per Million Living in each 
Age-period, 1861-70 and 1896. 



Death-rates . | 


Periods. 


All 
Ages. ' 


0- 


5- 


10- 


15- 20- 


25- 


35- ! 45- 


55- 


6:5- 


75 & up- 
wards. 


MALES. 


1861-70 
1890 


242 
618 


13 

27 


8 7 18 
23 19 42 


26 
48 


60 204 536 
89 419 1362 


1 
1201 1 1862 
3340 5427 


2258 
5992 


Percentajre Inc 
tween lS(il-70a 


•ease be- 
nd 1890. 


155 


109 


102 175 1 137 86 


49 


106 


154 


179 


177 


105 


FEMALES. 


Death-rates . | 


1861-70 
1890 


519 
901 


13 
32 


7 
11 


7 
11 


16 
30 


32 161 

42 175 


669 1530 
933 2308 


1 
2291 i 2791 
4187 5086 


1 2786 
6539 


Percentage Inc 
tween 1801-70 


rease be- 
aud 1896. 


74 


'loO 


60 60 


i 1 1 1 i 
91 33 ' 9 40; 51 83 104 


135 



241 



242 



VITAL STATISTICS. 



The mortality registered from cancer was two and a half times 
as great among males and one and three-quarter times as great 
among females in 1896 as that registered in 1861-70. Part at 
least of this increase is, however, only apparent, due to the 
imjoroved diagnosis and more careful statement of causes of death. 
This is shown (1) by the steady decrease in the number of deaths 
from tumour, abdominal disease, and other ill-defined forms of 
disease; and (2) by the fact that the increase of mortality from 
cancer is much greater among males than among females. (See 
table, p. 241.) 

This greater increase in the male mortality from cancer is most 
easily understood on the hypothesis that the rise is in great 
measure apparent and due to better diagnosis ; the cancerous 
affections of males being internal in a much larger proportion 
than those of females. Had the increase been altogether real, it 
is difficult to understand why it should affect males so much more 
than females. 

(3) The system of inquiry on the part of the General Register 
Office, when certificates of a dubious character are received, Avas 
the means of increasing the cancer death-rate in 1881-90 by 6 
per million. 

(4) Where more accurate statistics are available the increase in 
the cancer death-rate is seen to be on a smaller scale. Mr. 
George King, f.i.a., and the author have shown (Proe. Roy. Soc, 
vol. liv.) that Avhen the national statistics of England, Scotland, 
and Ireland are compared Avith those of lives insured in the 
Scottish Widows' Fund Life Assurance Society, the results 
depicted in Fig. 37 are obtained. 

Corrections for age-distribution have been made, to be hereafter 
explained. The importance of these corrections may be gathered 
from the following : — ■ 

Comparison of Corrected and Uncorrected Cancer 
Death-rates. 



Period. 


Not Corrected. 


Corrected. 


England. 


Ireland. 


England. 


Ireland. 


1860-66 . 
1867-73 . 
1874-80 . 
1881-87 . 
1888-90 . 


498 
597 
719 
902 
1091 


553 

627 

680 
807 
894 


625 

747 

911 

1152 

1393 


614 
661 
699 
824 
912 



244 VITAL STATISTICS. 

It will be observed that by the uncorrected figures Ireland 
stands a little above England for the first two periods, and a 
little below it for the other three, but- that no very great 
difference appears between the rates for the two countries. The 
corrected figures, however, show that Ireland stands below England 
throughout, so that in the first two periods the position of the 
countries is reversed by the correction, and in the last three 
periods the difierence in favour of Ireland is very great indeed. 
It is evident that the ordinary method of presenting the statistics 
exaggerates the rate of cancer in Ireland as compared with 
England, a result which might have been expected, owing to the 
age-distribution of the populations of the tAvo countries. 

The comparative immunity from cancer shown by the ^ Irish 
curves is probably caused, in part at least, by deficiencies of 
diagnosis and certification, associated Avith the sparsity of popula- 
tion and poverty of that country. For our present purpose the 
main interest of Eig. 37 lies in the Scottish "Widows' curve. 
This has the easiest gradient of all, strongly confirming the view 
that the apparent increase of cancer mortality is caused by 
increased accuracy in diagnosis and certification. The policy 
holders in the Scottish Widows' Ofiice are presumably Avell-to-do 
and able to secure on the whole better medical attendance than 
the mass of the people, and their death-returns consequently show 
to a less extent the effect of increased accuracy of diagnosis and 
certification. 

Another reason for thinking that the apparent increase in 
cancer is at any rate mostly due to improved diagnosis is derived 
from a comparison of the curves for males and females respectively. 
It will be noticed that the curves for females are always the 
higher, and that in each pair of curves the difference is practically 
constant throughout the entire period. JSToav, if there were a 
real increase of cancer, there is no sufficient ground for thinking 
that this would be confined to any one set of organs of the body, 
or would affect one sex more than another ; and in such case the 
difference between the cancer in males and females would be a 
percentage of the total, and would increase at the same rate as 
the curves themselves rise, and consequently the curves for males 
and females would tend to widen their distance apart. This, 
however, is not so. In each of the three pairs the curves for 
males and females do not diverge, but, if anything, tend to 
approximate. 

It may be urged that, notwithstanding what has been said 



MORTALITY FROM CANCER. 245 

above, cancer may have increased more in certain parts of the 
body than in others, and that, although it has really increased in 
both sexes, it has increased in such greater proportion among 
males, that the curves for the two sexes remain parallel. This 
vicAV, however, is contradicted by the Frankfort statistics given in 
the same paper. It is not necessary to reproduce these figures 
here. Briefly they show that when cancer deaths in that city are 
classified, as their very complete character enables them to be, 
into accessible, inaccessible, and cancer of undefined position, 
between 1860 and 1889 there has been no increase in the 
mortality from the cancer affecting positions in which it is easily 
accessible and detected. 

From the above and other considerations which cannot be 
detailed here, j\Ir. King and the author arrived at the conclusion 
that the evidence of increase in cancer-mortality is altogether 
insufficient, and that such increase has probably not occurred. 
The increase is, in other Avords, only apparent, being due to 
improvement in diagnosis and more careful certification of the 
causes of death. 

A recent writer has advanced the theory that the higher 
mortality from cancer is caused by the greater number of sur- 
vivors to what may be called the cancer-ages. This explanation 
implies a mental confusion between deaths and death-rates. When 
the death-rates at each group of ages, as on p. 241, are given, 
this point does not arise ; and when the death-rate is stated more 
generally, correction can be made by applying the death-rate at 
difi"erent age-grou})s to a standard population (as on p. 173), thus 
eliminating entirely the question of a larger number of survivors 
to higher ages. The statement that the decrease in the mortality 
from phthisis involves an increased mortality from cancer, implies 
the same mental confusion between mortality and rate of mortality. 
A method of applying this correction was described by Mr. King 
and the author in 1893 {pp. cit.). The standard population taken 
by them was that of the English Life-Table, No. 3, Persons, viz. : — 

Ages. Population. 

25-35 ..... 260,259 

35-45 ..... 232,106 

45-55 ..... 199,912 

55-65 ..... 158,812 

65-75 ..... 102,19(3 

75 and upwards . . . . 46,715 

1,000,000 



246 VITAL STATISTICS. 

The death-rates in the populations to be contrasted having heen 
obtained for the age-groups 25-35, 35-45, etc., they were each 
multipHed into the populations of the above table. The sum of 
the products for any particular period of years gave the number 
of deaths from cancer per annum among one million persons aged 
25 and upwards. Then, by comparing the same for, say, the 
period 1860-66 Avith that for the period 1881-87, we ascertain in 
which direction the apparent death-rate from cancer is progressing. 
By adopting this course in each instance, the observations for all 
the different localities and all the different periods of years are 
reduced to one common standard, and the errors are eliminated 
which would arise from variations in the age-distribution of the 
population. 

It may be interesting at this point briefly to describe the 
method by which the mean cancer death-rates for series of years 
were changed into figures for single years. This might have 
been accomplished by the application of analytical processes. 
The method adopted was an application of the graphical method 
of constructing life-tables. (See p. 265.) 

As showing the application of the method to the present 
inquiry. Fig. 38, relating to England and Wales, is given, of 
which a very few words of explanation will suffice. Along the 
abscissa axis are marked off equal lengths to represent each of 
the periods of seven years under review, with a portion of 
proportionate length for the three years 1888-90; and along the 
ordinate axis the rates of mortality per milhon are marked off. 
Rectangles are then erected, the areas of which are to represent 
the number of deaths from cancer in each of the septennial 
periods. Thus the area of the rectangle for the septennium 
1860-66 is 4375 for males, as its base is seven and its altitude 
625. Similarly for the other rectangles. 

Through the tops of the rectangles a continuous curve is then 
drawn in such a way that the area cut off is exactly equal to 
the area added. The length of the ordinate of the curve, which 
is central to any particular year, will then give the deaths from 
cancer in that year; and the accuracy of the drawing of the 
curve will be proved, if there be no sudden change of direc- 
tion, and if the sum of the numbers for the seven years of a 
septennium is equal to the area of the rectangle for that sept- 
ennium. Fig. 38 shows the curves for England and Wales, that 
for males being an unbroken line, and that for females a dotted 
line. Similar curves were prepared for all the observations, and 



MORTALITY FROM CAN'CP:R. 



24i 



these are collected in Fig. 37, so that they may be easily com- 
pared. 

In the Supplement to the Fifty-fifth Annual Report of the 
Registrar -General (p. liii. et mp) are given the results of the 




Fig. 38. 

Showing how the Cancer Death-rate for each year is obtained from the Mean 
Cancer Death-rate for Septennial-periods. 



calculation of the distribution of cancer mortality in the different 
English counties in terms of a standard million of population 
over 35 years of age. The result is some striking alterations 
of cancer death-rates. Thus, after such a correction has been 



248 VITAL STATISTICS. 

made, the cancer mortality of Huntingdonshire is to that of 
Durham as 127 only to 100, while the crude-rate at all ages 
is as 208 to 100. Similarly the difference between the crude- 
rates of Cornwall and London is only about 2 per cent., that 
of their corrected rates 38 per cent. 

The local distribution of cancer in England and Wales in 
1881-90, calculated by the corrected method indicated above, 
is given on p. Iv. of the last decennial supplement. The average 
annual death-rate of a standard million, above 35 years of age, 
in England and Wales M^as 1844. The highest cancer death- 
rates were London, 2250; Huntingdonshire, 2157; Cambridge- 
shire, 2012; Sussex, 1999; Warwickshire, 1976; the lowest, 
Monmouthshire, 1574; Dorsetshire and Buckinghamshire, 1578; 
Derbyshire, 1597; Wiltshire, 1604; and Cornwall, 1630. The 
high corrected cancer death-rate of London, like that from 
phthisis, is largely due to the presence of hospitals for the 
special treatment of these diseases. The above correction, it 
will be noted, is for variations of age-distribution, not for the 
presence of hospitals attracting patients from other districts. 

Heredity in Cancer. The fact that several members in suc- 
cessive generations of a given family have died from cancer is 
commonly accepted as proof that the disease is hereditary. This 
is far from being the case. Cancer causes a certain average 
number of deaths among a given number of persons. The 
death-rate from cancer, as will be seen from the table on p. 241, 
is insignificant until the age of 35 is reached, rapidly increasing 
at each higher age-period. On the basis of the national figures 
for 1887-89, one out of twenty-one men and one out of twelve 
women, who reach the age of 35, die eventually of cancerous 
disease. {Fifty-second Annual Report of the Registrar-General, 
1889, p. xiv.) Eor the following remarks on this important 
point, I am indebted to Mr. G. King, f.i.a. Given a certain 
probability of death from cancer, and knoAving the number of 
a family, it is easy to calculate the probability of one, two, or 
more of them dying of cancer quite independently of heredity. 
Even if heredity were proved to be absolutely inoperative, it is 
certain that there would be families among whom numerous 
deaths from cancer would occur. It does not prove heredity 
to show that in one family, five deaths, say, occurred from 
cancer. This might happen from mere chance, and in fact 
such cases must occur without heredity at all. De Morgan 



MORTALITY FROM DIABETES, ETC. 249 

worked out the probability of 1000 successive heads being 
thrown in tossing a coin, and he showed that given a sufficient 
number of people starting to toss coins, it was a certainty that 
at least one of them would toss 1000 consecutive heads. So, 
given a sufficient number of families, it is a certainty, even if 
there be no such thing as heredity, that of at least one family, 
say ten members Avill die of cancer. The only absolute proof 
of heredity would be to show that cancer occurred frequently in 
certain families, and practically nowhere else ; short of this the 
prolmbility of heredity of cancer would be increased if it could 
be shown that cancer was much more common in certain families 
than in the average for the whole community, due allowance 
being made for variations in age and sex-distribution. 

Diabetes. The registered death-rate from diabetes mellitus has 
steadily increased during the last twenty years. In 1895 it was 
75, and in 1896 it Avas 74 per million, as compared Avith 41 
in 1877. The death-rate for males in 1896 Avas 83, and for 
females, 66 per million. 

Much of this apparent increase is doubtless due to greater care 
in diagnosis and in certification ; but it is also suggested that 
there has been a real increase due to the increased mental strain 
and Avorry of modern life, a similar explanation being given for 
the registered increase of chronic renal disease. 

The question as to whether there has been any real increase 
must still be left undecided. The disease is chiefly fatal after 
the tAventy-fifth year of life. In 1881-90, the death-rates among 
males at the age-periods 45-55, 55-65, 65-75, and 75 and 
upAvards Avere equal to 134, 282, 397, and 314 per million living, 
as compared Avith 96, 181, 247, and 172 in 1871-80. 

The mean annual mortality from diabetes in England and 
Wales is stated in the Reijistrar-General's Forty-ehjliili Animal 
Report, 1885, to be 26 per cent, above that of Scotland, and 40 
per cent, above that of Ireland. This is in accord Avith the 
distribution of diabetic mortality as shoAvn in the same report, 
Avhich aj)pears to shoAV a remarkable inverse relation betAveen 
the amount of diabetes and the amount of rainfall. 

Dietetic Diseases. These are deaths from deficiency of diet 
(scurvy, starvation, Avant of breast-milk) and intemperance, em- 
bracing chronic alcoholism and delirium tremens. In 1896, these 
diseases gave a registered death-rate of 80 per million living, 68 



250 



VITAL STATISTICS. 



of which Avas attributed to intemperance, The deaths returned 
under this head are, however, not trustAvorthy ; alcoholism causes 
in reality an enormously greater mortality than is ascribed to it. 

In 1861-65, the mean death-rate registered as caused by intem- 
perance was 42 per million. It steadily increased, in 1891-95 
reaching 68 per million. This increase is almost certainly due 
to more correct certification of deaths. 

One of the commonest diseases clue to alcoholism is cirrhosis of 
the liver ; and as this is the chief cause of mortality under the 
heading "liver diseases and ascites," the latter may be taken as a 
fairly correct index of the amount of alcoholic excess in England 
and Wales. 

Annual Death-rate per Million Persons Living from Diseases 
OP THE Liver and Ascites. 



Period. 


3 years. 
1858-60. 


5 years. 
1861-65. 


5 years. 
1866-70. 


5 years. 
1871-75. 


5 years. 
1876-80. 


5 years. 
1881-85. 


5 years. 
1886-90. 


5 years. 
1891-95. 


Death-rate per ^ 
million . j 


394 


416 


418 


428 


424 


372 


325 


270 



It Avill be seen that the mortality from liver diseases has been 
declining for some years, and this coincides with Avhat is known 
of the imj)roved alcoholic habits of the community. Here, again, 
difficulty arises Avhen an attempt is made to subdivide liver 
diseases. Thus the death-rate per million ascribed to cirrhosis 
among males has increased from forty-three in 1861-70 to 140 in 
1881-90; that ascribed to ascites has decreased from tAventy-six 
to nine, and that from other liver diseases has decreased from 366 
to 210. It is probable, on the AAdiole, that there has been a 
decline in alcoholism and its consequences, notAvithstanding the 
registered increase in cirrhosis of the liver. 



Developmental Diseases. The following table shows that the 
death-rate from premature birth and from congenital defects has 
steadily increased, being higher in 1896 than in any previous 
year. The best Avay to estimate the number of deaths resulting 
from premature birth and from congenital defects is in jyropm^tion 
to tlie total mmiber of hirtlis, as in the following table. By this 



MORTALITY FROM DEVELOPMENTAL DISEASES. 251 

means, tlie disturbing influence of the low l)irth-rate in recent 
years is removed. 







Deaths to 1000 Births. 


Death-rate per 
million Persons. 

Old Age. 




Premature Birth. 


Congenital Defects. 


1861-65 . 
1866-70 . 
1871-75 . 
1876-80 . 
1881-85 . 
1886-90 . 
1891-95 . 
1896 . 




11-19 
11-50 
12-60 
13-38 
14-18 
16-15 
18-42 
18-99 


1-76 

1-84 
1-85 
2 39 
3-23 
3-39 
3-87 
4-16 


1353 

1276 

1-207 

1072 

1014 

976 

929 

850 



The total infantile mortality in 1896 was 148, and in the ten 
years 1886-95 it also averaged 148 per 1000 hirths. It may be 
surmised that as the infantile mortality from all causes together 
has not increased, part of the increased mortality from premature 
birth is only apparent, and due to transference from other headings. 
Some influence may also be ascribed to the markedly increased 
employment of women in industrial occupations. 

The above table shows a falling off in the death-rate from old 
age. If this Avere a real falling off, it would not be an indis- 
putable advantage, as most people would prefer to die of old age. 
The decline under this head is, however, chiefly due to an improved 
specification of the causes of which the old die. The mortality 
from "old age" is always higher in cold seasons, cold being the 
special enemy of the old, as heat is of the young. 

Diseases of the Nervous System show a death-rate per million 
of 1546 in 1861-65, and of 1600 in 1891-95, the highest being 
1808 in 1881-85. Convulsions as a cause of death are properly 
not included in the above, the death-rate ascribed to this cause 
having declined from 1258 in 1861-65 to 688 in 1891-95. 
Diseases of the Circulatory System liave increased in registered 
mortality from 997 per million hi 1861-65 to 1677 in 1891-95. 

Much of this increase is probably due to transference from such 
headings as debility, old age, and the like, an assumption which is 
supported by the fact that the main increase is in the later age- 
periods. Thus at the age-period 75 and upwards the death-rate 



252 



VITAL STATISTICS. 



per million from these diseases has increased from 9186 in 
1861-70 to 18,864 in 1881-90, while at the age-period 25-35 the 
increase is only from 1019 to 1345. Some of the increase is also 
possibly due to the institution of letters of inquiry from the 
General Register Office when " dropsy " was returned as the cause 
of death. Whether there is any real increase not explained by 
the preceding or similar considerations is still dubious. 

Urinary Diseases caused a death-rate per million living of 
453 in 1891-95, as compared with 246 in 1861-65. We have 
also to bear in mind the diminution under the heading " dropsy " 
in connection with the registered increase under this heading. 
The uncertain amount of allowance for transference of diseases 
(due to better diagnosis or more careful certification) is a stumbling- 
block at every step. The weighty remarks of the Registrar- 
General on this point may be quoted : " To be without trust- 
worthy means of comparison is doubtless an evil, but to ignore 
the differences and to deal with the records as thoroughly reliable 
would be still worse, for it is far better to be without statistics 
at all, than to be misled by false ones." 

Violence. The following table shows the death-rate from the 
various forms of violence in successive year-periods. 

Mean Annual Death-rate per Million Living from Violence. 





1S61-65. 


1860-70. 


1871-75. 


1876-80. 


1881-85. 


1886-90. 


1891-95. 


















Negligence ( 


690 


678 


671 


630 


580 


544 


564 


Homicide 


19 


19 


17 


14 


13 


11 


10 


Suicide . 


65 


66 


66 


74 


75 


79 


89 


Execution 


0-8 


0-4 


0-4 


1-0 


0-4 


0-8 


0-4 



The death-rate from violence is much greater in the male sex. 
Thus in 1881-90 it averaged 968 among males, and 347 among 
females. The excess among males is not solely due to occupational 
dangers, as it is seen in the first five years of life, in which the 
death-rates per million in the two sexes are 1266 and 1019 re- 
spectively. The death-rate from accident has gradually declined, 
but suicide is on the increase. 



MORTALITY FROM VIOLENCE. 



253 



The relative incidence of the various forms of accident or 
neghgence in the two sexes can be gathered from the following 
figures for 1896 : — 

Death-rate per Million Living of each Sex from Accident 
OR Negligence, 1896. 





Males. 


Females. 


In Mines and Quarries 


70 





Vehicles and Horses .... 






144 


18 


Ships, Boats, and Docks (not Drowning) 






17 





l^nihling Ojjcrations .... 






15 


— 


Machinery ..... 






13 


1 


Weapons and Implements . 






8 


1 


Burns and Scalds .... 






74 


93 


Poisons, Poisonous A^apours 






27 


14 


Drowning ..... 






135 


25 


SnH'ocation ..... 






78 


66 


Falls 






101 


74 


AVeather Agencies .... 






13 


4 


Otherwise, or not stated 






86 


32 


Total 






781 


328 



The proportion of the different forms of suicide in the two 
sexes can l)e gathered from the following table, which deals Avith 
actual deaths not death-rates in England during 1896 : — 









Deaths from Suicide, 1896. 




Males. Females. 


Vehicles and Horses 

{a) Railways 

(b) Vehicles other than railwa 
AVeapons and Implements 
Burns, Scalds, and Explosives 
Poisons and Poisonous Vapours 
Drowning .... 
Suffocation .... 

Falls 

Otherwise, or not stated 


ys 




94 

3 

551 

2 

279 

347 

602 

49 

52 


14 

78 

3 

193 

207 

139 

20 

23 


Total 






1979 


677 



254 



VITAL STATISTICS. 



The poison most commonly employed for suicidal purposes is 
carbolic acid, 88 and 75 in the two sexes, next opium and its 
derivatives (39 and 17), then prussic p,cid among males (24), and 
strychnia among females (12). Nearly all the deaths from 
suffocation are by means of hanging. 

Suicide in different countries. According to figures published 
by Bertillon,* suicides are most frequent in Saxony, Denmark, 
and Switzerland, as shown in the following table : — 





Period of ^ 


Number of Annual 




Observation. Suicides per Million 
Inhabitants. 


Saxony . 


1878-82 


392 


Denmark . 


1880-82 


251 


Switzerland 


1878-82 


239 


Baden 


1878-82 


198 


Wnrtemburg . 


1877-81 


189 


France 


1878-82 


180 


Prussia . 


1878-82 • 


166 


Belgium . 


1878-82 


100 


Sweden 


1878-82 


9-2 


England and Wales . 


1878-82 


75 


Norway . 


1878-82 


69 


Scotland . 


1877-81 


49 


Ireland 


1878-82 


17 


* C 


p. cit., p. 119. 





CHAPTER XXII. 

LIFE-TABLES. 

LIFE -TABLES afford an accurate means of measiiring the 
probabilities of life and death. They represent " a genera- 
tion of individuals passing througli time," the data on which 
they are founded being the number and ages of the living, and 
the number and ages of the dying. Dr. Farr calls the life- 
table a hiometer, and speaks of it as of equal importance, in all 
inquiries connected with human life or sanitary improvements, 
with the barometer or thermometer and similar instruments 
employed in physical research. It is the keystone or pivot on 
which life assurance hinges, converting it from a mere lottery 
into an accurate science. 

Addison, in his " Vision of Mirza," possibly writing with 
Halley's graduated Life-Table before him, gives the following 
allegory : — 

"The bridge tliou seest, said lie, is Human Life; consider it 
attentively. Upon a more leisurely survey of it, I found that it 
consisted of threescore and ten entire arches, with several broken arches, 
which, added to those that were entire, made up the number about an 
hundred. As I was counting the arches, the Genius told me that this 
bridge consisted at first of a thousand arches; but that a great flood 
swept away the rest, and left the bridge in the ruinous condition I 
now beheld it. But tell me furthei", said he, what thou discoverest 
on it. I see multitudes of jjeople passing over it, said 1, and a black 
cloud hanging on each end of it. As I looked more attentively, 1 
saw several of the ])assengers drojiping through the bridge into the 
great tide that flowed underneath it : and upon further examination 
perceived that there were innumerable trap-doors that lay concealed 
in the bridge which the passengers no sooner trod upon, but they fell 
through them into the tide, and immediately disajipeared. These 
hidden pit-falls Avere set very thick at the entrance of the bridge, so 
that throngs of peoj^le no sooner break through the cloud, but many of 
them fell into them. They grew thinner toicurds the middle, but 
multiplied and laid closer together towards the end of the arches that 

255 



256 VITAL STATISTICS. 

were entire. There were, indeed, some persons, but their number was 
very small, that continued a kind of hobbling march of the broken 
arches, but fell through one after another, being quite tired and spent 
with so long a walk." 

This graphic narration of the "hidden pit-falls and trap-doors," 
and the " broken arches," which beset the course of human life, 
illustrates with beautiful simplicity the facts contained in this and 
the next three chapters. 

Description of Life-Table. The essential portions of a life- 
table are the number and ages of the living and the number and 
ages of the dying. 

(1) Suppose that we could observe a million children, all born 
at the same moment, and follow them throughout life, entering 
in a column the number who remain alive at the end of each 
successive year until all have died. This column is headed by 
the symbol l^; where l^ represents the number who reach the 
precise age x. 

In the second column we record the number dying before the 
completion of each year of life. Thus the number Avho die 
before reaching the first anniversary are placed opposite the age 
in the table, and so on. In this way Ave obtain the column 
headed d^; where d,, represents the number out of l^ persons 
attaining the precise age x, who die before reaching the age 
ic-fl. It is evident, therefore, that — 

dx ^= l'x~ f'x+l 

i.e., the number dying between the ages x and icH-1 is equal 
to the difference between the numbers living at the ages x and 
x+1. 

In practice it is not possible to observe a body of children 
throughout life in the precise manner indicated, so that other 
methods must be resorted to. 

(2) It is not necessary to assume, as in the preceding case, 
that all the persons observed have been born at the same time. 
If we could trace any million children throughout life, hoAvever 
various might be the dates of their births, a life-table might be 
similarly constructed, if the numbers living and dying during 
each year of life were knoAvn. 

Our national records do not lend themselves to either of these 
methods, but the Institute of Actuaries H.^- (Healthy Males) 
Table, Avhich is used by the best assurance societies in this 



LIFE-TABLES. 257 

country as the basis of their calculations, is partially based on the 
second method ; being constructed from the results of watching 
a large number of insured lives from the time of their insurance 
to death. 

(3) Without tracing the history of individuals through life, 
we may, by taking a complete census of the population, distributed 
according to age and sex, obtain data for forming the column 
l^. Similarly from the annual death-returns, we obtain the 
number dying during each year of life in a given year, and thus 
form the column d^. 

The methods by which the other necessary columns of a life- 
table are derived from these two fundamental columns will be 
described shortly. 

(4) The method usually adopted in constructing a life-table is 
a modification of the last. The mortality experience of a single 
year may be exceptional in character. For this reason the number 
of persons dying within a longer period, e.g., in the decennium 
1881-90, and their ages at death are observed. In the same way 
the population out of which these deaths occurred is ascertained 
by calculation from a single census, or by combining the results of 
two census enumerations, as described hereafter. It is assumed 
that the rate of mortality {i.e., the number of deaths per iinit of 
popidation) for any age of life thus obtained will be applicable to 
other persons out of a given number started with at birth, as they 
successively attain the age in question. By this means results are 
obtained which, being wholly based on recent observations, are 
more correct, as indicating the present conditions affecting the 
duration of life, than if a million persons were watched from 
birth to death ; for, in the latter case, the conditions which de- 
termined the rate of mortality might, before the series was available, 
have undergone great changes, and for practical purposes the table 
be almost valueless. 

Dr. Farr's English Life-Table, No. 3, Avas based on the regis- 
tered deaths in England and Wales during the seventeen years 
1838-54, and on the two census enumerations of population in 
1841 and 1851. Dr. Ogle's Life-Table is based on the mean popu- 
lation of England and Wales of the decennium 1871-80, and on 
the total deaths during the same decennium, and Dr. Tatham's 
Life-Table on the corresponding figures for 1881-90. 

Method of Construction of Life-Table. It is evident that the 
deaths in a population, during any stated year, do not occur 



258 VITAL STATISTICS. 

simultaneously either at the beginning or the end of the year, but 
are distributed throughout its course. It is also evident that the 
deaths registered at any age x will not have occurred at the precise 
age aj, but some will have just attained the age x, whilst others 
will have been close on a;+l. Now it is assumed, in the usual 
method of constructing a life-table, that the deaths at age x 
occur at equal intervals throughout the ensuing year, an assumption 
the error of which is infinitesimal, except for the first two years 
of life. 

We have seen that l^ in the life-table is the number Avho, out 
of a given number born, attain the precise age x. The number 
?i) represents the number surviving to the end of their tenth year 
out of a given number l^ at birth. But in a population situated 
as just described, persons will be found whose ages are of various 
intermediate periods between x and a: + 1, or in the instance taken, 
between ten and eleven years. If, however, we assume the deaths 
to be equally distributed throughout the year, the number who 
attain its middle will be the arithmetical mean of those com- 
mencing the year and those completing it. Thus : — 

The number who attain the middle of the tenth year of life 
is Z^oj = |(Zjo + ^ii). The mean population thus obtained is denoted 
by P^* and the deaths extracted from the registers by d^. 

If now we divide the deaths registered at any year of age {d^) 
by the mean population found existing at that year of age (P^), 
we shall ascertain the rate at which the population is dying in the 
centre of that year of age. Thus we have : — 

~ = lUy. where m^ = rate of mortality per unit of population, f 

iVe have already stated that the life -table enables us to 
measure the probabilities of life and of death ; and, conversely, 
having given these probabilities, we can construct the life-table. 
We must first, however, see how these probabilities may be 
calculated from the rate of mortality (ju^) already obtained. 

* It is known as Lx in actuarial works. The above is Dr. Fair's notation. 

t The ratio of deaths to mean population, or m^, has been called by Farr 
the rate of mortality, and we follow his notation and system ; but actuarial 
writers reserve the name rate of mortality for the probability of dying within 
a year (5'^). The name central death-rate has been given by these writers to 
m^, because it represents the rate at which people are dying in the centre of 
the year a; to ar -1-1, 



LIFE-TABLES. 259 

[Now the probability of an event occurring is represented by a 
fraction whose denominator is the number of possible events, and 
numerator the number of favouraljle events. Thus, if there are 
eight balls in a bag, of which three are black and five white, the 
prol«ibility of drawing a white ball is found us follows. The number 
of possil)le drawings is eight, inasmuch as any one of the balls may 
be drawn, but only five of these would be favourable. Hence the 
probability = g. 

The proljability of drawing a black ball = l - § = ^. 

Reverting now to the symbols and conditions of the life-table, 
let h = number of persons living at the beginning of the year x, 
of whom /x+i survive to the end of the year. The probability of 

lx-\-\ 

anyone living to the end of the year is therefore ^7 — ; and inasmuch 
as dx die during the year, the j)robability of anyone dying during 
the year is--^. 

Ix 

If we indicate by fx the ])robability that a person of the precise 
age X will survive one full year, and by qx the probability that the 
same person will die within one year, then — 

Ix+l 

^'- = 17 

dx 

qx = j 
ix 

Thus the jirobability of ^ mimber of survivors at end of year 

living through one year / ~ number living at beginning of year 

^x+l Ix-dx 

ix tX 

" This may be expanded into 

Ix - dx {Ix - ^ dx ) - ^ dx 
Ix \lx ~ 5 dx) -f 5 dx 

On the assumption of a uniform distribution of deaths, the 'mean 
population ' of the year is obtained by deducting one half of the 
deaths occurring in the ensuing year from the precise number living 
at age x. 

Hence, Ix - -^ dx, which may also be written ^ (Ix+lx+i) 
= the mean population for the year, which is denoted by Ix+i. 

Therefore jJx =^*— f^^ 
h+i + idx 

Dividing each term by Ix+i, we obtain — 

1 1 dx 

P""^ 17 

-l-x+h 



260 VITAL STATISTICS. 

-r, ^ ^. c . • dx number dying at age x 

But tlie fraction -^^ = ^-^. f = mx 

Ix+i mean popiilation at age x 

i.e., the rate jjer unit at which people are dying in the middle of the 
year of age x to a; + 1 ; and this is the same rate as that previously 
arrived at by dividing the dx of the death-registers by the 2^x ascer- 
tained by enumerating the popvilation."] Hence we have— 
_ 1 --^nix _2-mx 
l+^iix 2 + mx' 

By this formula a very simple relation is found to exist between 
the probabilities of life and the rate of mortality. Having, from 
the census returns and the death registers, obtained the ratio 
m^ for all values of x (i.e., all ages), we can by the above formula 
find j9^, and thence we can, by continued multiplication, construct 
the life-table. 

This method may be made clearer by an example. The entry 
in the ?>?,. column is obtained by dividing the deaths during the 
year by the mean population. From the entry in this column j^xi 
or the probability of living one year, is obtained by the formula 

^wj--?%^ Thus at birth the probability of a male living one 
^^ 2 + m^ 

9 _ .1 QQOfi 

year is, by Farr's English Life-Table, ""g = -83212, and for 

each year in the series the probability of living one year is 
obtained in the same way.* 

The next column {Q is obtained by multiplying the number 
living at the immediately preceding year by j)x- Thus, starting 
with 511,745 males at birth, the number living at the end of 
one year is obtained by multiplying the probability of surviving 
to the end of the first year by this number (l-^ = Iq xjj^) 
511745 X -83212 = 425358-6. 

• These two steps can he combined, and much labour saved by the 
following method : — 

Since mx=^^ («) and 

2 -nix /T.\ 
2 + m^ 
Therefore by substituting from (a) 

~P 2P -d P -Id 



^''~2 + d~2P^+d^ P^ + id^ 
Z.P 



LIFE-TABLES. 261 

This process is shortened by logarithms as follows: — 

Log. 511745 = 5-7085692 
Locr. •8:3212 = 1-9201860 



Log. of product of these two = 5-6287552 
Therefore product = 425358-6 

The next column in the life-table is one showing the mean 
number living in each year of life (P^)- It is directly derived 
from the I^. column. Thus the mean number living in the 

twenty-first year = ^° t> "^ ' 

The next column in the table is known as the Q^ column. 
The number opposite any age in this column is the sum of all 
the numbers in the P^ column from that age to the end of the 
table, i.e., until all the lives become extinct; and it shows, there- 
fore, the aggregrate number of years which the persons at each 
age in the table will live. 

Q, = P^ + P,+i + P,+2 + etc. + P,+„ 
where x + ji = the last age mentioned in the life-table.. 
From the column {Q^), and the l^ column, the mean future 
lifetime (expectation of life) of any person can be obtained by 

the formula E^ or e°^ = -^. 

''X 

In the preceding remarks it has been assumed that the pojiula- 
tion and the deaths at each individual age are known. In practice 
this is not the case. The census reports and the annual death- 
returns state the population and deaths in groups of ages. Even 
if the number living and dying during each year of life were 
given, the numbers would probably, from imperfections in the 
returns, be less accurate than those obtained by interpolation, 
effected either by mathematical calculation or by the graphic 
method to be shortly described. The graphic method is not 
applicable to the first five years of life, for which a special plan of 
interpolation described in the following example is required. 

Details of Construction of Life-Table. In the following 
description the figures used in tlie life-table for Brighton are 
employed as an example. 



^62 



VITAL STATISTICS. 



Metliod of ascertaining Population and Deaths for each Year 
of Age. — 111 the construction of a life-table Ave must have an 
accurate statement of 

(1) The population for each year of age; and 

(2) The number of deaths at each year of age occurring during 
the corresponding year in each sex, in order to ascertain the death- 
rate holding good for each year of life. 

These data not being supplied in full for each year either for 
population or deaths, the means for interpolating the correct 
figures for each year of life from the figures furnished in the 
followiner table must be first given. 



Population of the Parliamentary Borough of Brighton. 


Deaths in 


the Parlia- 








mentary Borough of 
Brighton, Jan. 1st, 1881, 








Age. 


Census, 1881. 


Census, 1891. 


to Dec. 31st, 1890. 


Males. 


Females. 


Males. 


Females. 


Males. 


Females. 


0- . 


7233 


7374 


7046 


7051 


4569 


3800 


f>- 




6653 


6435 


7137 


7169 


333 


301 


10- 




6158 


6473 


6829 


7300 


149 


174 


15- 




5258 


8069 


5882 


8600 


229 


243 


20- 




5158 


8023 


4967 


9038 


256 


292 


25- 




8471 


12291 


9142 


13894 


678 


709 


35- 




6260 


8889 


7308 


10411 


872 


866 


45- 




4557 


6698 


5335 


7755 


1040 


1034 


55- 




3174 


4819 


3574 


5443 


1104 


1243 


65- 




1645 


2807 


2254 


3451 


1235 


1577 


75- 




663 


1041 


778 


1291 


945 


1416 


85- 




76 


118 


85 


221 


261 


413 


95- 




3 


4 


4 


5 


7 


22 


Total all 


55309 


73041 


60341 


81629 


11678 


12090 


H 


;es 


128350 


141970 



(1) To ascertain the total numher of lives at-rtsh at each group 
of ages during the decade 1881-90. — We must first ascertain the 
central population in each group by adjusting the figures in the 
above table to June 30th (the census being taken at the end of 
the first quarter of the year). 

The formula is Q' = P R^ where Q' = central population required ; 
P = census population ; and P = population resulting per unit per 



LIFE-TABLES. 



263 



annum. R is first found from tlie formula Q = PR^^, as in the 
calculations on p. 6. 

Value of E for each Age-period. 



Mai. s. 


Females. 


Age. 


Value of R 
for eacli 

Age-period. 




Value of R 

for each 
Age-period. 


Age. 


0- 
5- 
10- 
15- 
20- 
25- 
35- 
45- 
55- 
65- 
75- 
85- 


7046 = 7233 7^1" 
7137 = 6653 7v"" 
6829 = 6158 7^1" 
5882 = 5258 Ai" 
4967 = 5158 7^1" 
9142 = 8471 7i:i" 
7308 = 6260 7^1" 
5335 = 4557 A'l" 
3574 = 3174 7^1" 
2254 = 1645 7^1" 
778= 663 7^1" 
89= 79 7^1" 


-99738 
1-00705 
1-01040 
1-01128 

-99623 
1 -00765 
1-01560 
1-01590 
1-12600 
1-03200 
1-01610 
1-01200 


7051 = 7374 721" 

7169= 6435 7^1" 

7300= 6473 7^1" 

8600= 8069 Ai" 

9038= 8023 7i'" 

13894 = 12291 7i:'" 

10411= 8889 72'" 

7755= 6698 7i'i" 

5443= 4819 7^1" 

3451= 2807 721" 

1291= 1041 721" 

226 = 122 ^1" 


•99553 
1-0109 
1-0121 
1 -0064 
1-0120 
1-0123 
1 0159 
1-0148 
1-0123 
1-0209 
1'0217 
1-0636 


0- 

5- 
10- 
15- 
20- 
25- 
35- 
45- 
55- 
65- 
7.5- 
85- 



N^ext Ave find Q! the central population from Q' = PE^ where 
P is the census population and R is given in the above table. 

'^^''■^^=~ a' = 7233 (-99738)* 

log. 7233 = 3-859318 
ilog. •99738 = 1-999716 
log. (3' = 3-859034 
.'. Q = 7228 = central male population, 1881, aged 0-5. 
The central populations for each census year thus obtained are 
as follows : — 



1881. 


1891. 


Age. 


Males. 


Females. 


Males. 


Females. 


Age. 


0- . 


7228 


7366 


7041 


7043 


0- 


5- 






6665 


6452 


7150 


7188 


5- 


10- 






6-174 


6492 


6847 


7322 


10- 


15- 






" 5273 


8082 


5898 


8613 


15- 


20- 






5153 


8047 


4962 


9065 


20- 


25- 






8487 


12328 


9159 


13936 


25- 


35- 






6284 


89-24 


7336 


10452 


35- 


45- 






4575 


6724 


5356 


7783 


45- 


55- 






3184 


4834 


3585 


5459 


55- 


65- 






1658 


2822 


2272 


3469 


65- 


75- 






666 


1046 


781 


1298 


7.5- 


86- 






79 


124 


89 


229 


85- 



264 VITAL STATISTICS. 

Having now ascertained the central population for the two 
census years 1881 and 1891, we proceed to ascertain the total 
population for the ten years 1881-90, i.e., the total number of 
lives subjected to a year's risk of death during this period. 

The method by which the value of R has been calculated for 

each age-period is sufficiently indicated in the table p. 263. 

In calculating the total population for the years 1881-90, i.e., 

the total number of lives at risk in the period embraced by 

life-table, the following method has been adopted. Employing 

the notation already explained, the population for each year of the 

decade would be denoted by P, PR, PR^, etc. . . . PR"^. These 

amounts give the terms of a geometric series, of which the first 

term is P and common ratio is R. Hence the total population for 

the decade is the sum of this series, P + PR 4- PR^ + etc. + PR^, 

R'° - 1 
the usual formula for which gives a sum to ten terms = P „_ ^ 

_ PR'° - P _ Population, 1891 - Population, 1881 
R-l annual increase per unit 

By means of this formula the total lives at risk can be 
ascertained. The number at risk at each age-period can be 
ascertained either (a) by applying the same method to each age- 
period, or (b) the method described on page 281 may be adopted. 
Thus in the third age-period the male jjopulation for 1891 = 
6847, and for 1881=6174. The difference is 673. Also for 
that period ii- 1-0104. 

673 

Therefore total population = --——- = 64,712. A similar calcula- 

•0104 

tion gives us the results contained in the following table for the 

other age-periods. 

It is plain that when R is less than unity, the population for 

1891 will be less than that for 1881, so that numerator and 

denominator of the above fraction will always have the same 

sign. 



LIFE-TABLES. 



265 



Total Number of Lives at Risk in the Ten Years 1881-90, 
AND Total Number of Deaths during the same Period. 



Age. 




Number of Lives 
at Risk. 


Deaths. 


Mean Anmial Death- • 

rate for each Life 

at risk. 




Male. Female. 


Male. 


Female. 


Male. 


Female. 


0- 

5- 
10- 
15- 
20- 
25- 
35- 
45- 
55- 
65- 
75- 
85- 
95- 






71374 

69236 

64712 

55408 

506C3 

87843 

67436 

49119 

33698 

19187 

7143 

878 

34 


72259 

67524 

68595 ! 

8'2969 

84833 

130732 

96101 

71568 

510'20 

30957 

11613 

1589 

44 


4569 

333 

149 

2-29 

256 

678 

872 

1040 

1104 

1235 

945 

261 

7 


3800 

301 

174 

243 

292 

709 

866 

1034 

1243 

1577 

1416 

413 

22 


•06401 
•00483 
•00230 
•00413 
•00505 
•00772 
•01294 
•02117 
•03276 
•06436 
•13229 
•29726 
•20588 


•05259 
•00445 
•00253 
■00292 
•00344 
•00542 
•00901 
•01444 
•02436 
•05093 
•12192 
•25991 
•50000 


Total . 


576731 


769803 


11668 


12090 


•02024 


■01575 



Note. — Tlie ages are read thus : and under 5, 5 and under 10, 10 and under 15. 

(2) Having noAV obtained a statement of the total number of 
lives at risk and number of deaths in quinquennial and decennial 
groups of ages, the process by which the corresponding numbers 
for individual years of life have been obtained, must be examined. 
There are two chief methods by which the number for the indi- 
vidual years of each age-period can be " interpolated." 

{a) By the "method of finite diff'erences" applied to the 
logarithms of the figures representing the population and deaths 
at the beginning and end of each age-period. This method, 
known as the analytical, involves complex calculations for a 
description of which reference may be made to p. xxv. of Dr. 
Farr's English Life-Table No. III. Dr. Farr's methods have 
been somewhat modified and improved in the calculation of the 
Life Table for England and "Wales in 1881-90 {Decetmial Supple- 
ment of the Eeijistrar-General, part i.). 

(h) By the "graphic method" here adopted. This method 
was described in a paper by INIr. George King, f.i.a., in the 
Journal of the Institute of Actuaries, 'No. cxxxi. (October, 1883), 
" On the ^Icthod used by ]\Iilne in the Construction of the 



266 



VITAL STATISTICS. 



Carlisle Table of MortaMty." In this paper Mr. King cleared 
up the mystery which had hung over the method pursued by 
Milne in the construction of the Carlisle Life-Table, and showed 
that the method pursued was a graphic one identical with that 
here described. 

POPULATIOM-MALES. 























































_^^ 












i 
























4- 


\ 








-I" 


>' 






Arcu 

7 '.37* 






\^ 


f 


















\ 


\ 














Area 


6. 




\ 


9 
















8,784-3\ 












Atm 

55,403 


Area 

50,663 


Area 

87.843 


k 














G.ooo 


6.7<3-li\ 


.000 
















\ 
Area 
87.843 


l.gii.pX^ 












.000 


















Area 
49,119 


3.369.8 \ 


^ 










s 


1 






e 


r 






Area 
I 33,69s 

! 


».9i8.^S^ 

Area 
19,187 


\^ 714.3 


Area 

.^ 878 


Area 

3+ , 




Area ^^^^^ 












S-20 


20-25 


25-35 


35-45 


46-55 


56-65 


66-75 


75-85 


85 95 


95 & upwards 



Fig. 39. 



The method may be briefly described as follows : Along the 
abscissa line^Z (Fig. 39) mark olf five equal portions, each to 
represent five years, for the first five quinquennial intervals of 
age ; and let eight other equal portions, each of double length to 
represent ten years, succeed them for the subsequent decennial 
intervals of age. 

At each of the points A and B erect perpendiculars to AZ, and 



LIFE-TABLES. 



267 



make the perpendicular lines of such a height, in accordance with 
the marginal scale previously decided upon, that the parallelogram 
Ah shall equal in dimensions the population living aged 0-5. 
Thus in the diagram Z.V;= 14274-8, and this when multiplied by 
5, the number of years included between A and 5 = 71374, the 



DEATHS-MALES. 




05 5-10 10-15 



number of male lives at risk at ages 0-5. Similarly Cc = 13847-2, 
and this when multiplied by 5, gives 69,236 as the area of Be. In 
the later groups 10 years are taken. Thus 6^^/ = 8784-3, the area of 
F(j being'87,843. Having thus plotted out the populations living 
at various groups of ages, the number living at each single year of 
life is obtained as follows : — 



268 VITAL STATISTICS. 

A curved line is described through the parallelograms already 
drawn, sweeping as easily as possible through the upper part of 
these parallelograms from A to Z. This curved line (1) must be 
as little curved as other conditions will admit of. (2) It must 
never change its direction abruptly so as to form an angle in its 
path. (3) The curved line thus described must so cut each of the 
parallelograms that the area included between the base line below, 
the corresponding portion of the tAVO ordinates laterally, and the 
portion of the curved line above, shall equal the area of the 
parallelogram erected on the same base. Thus the area of the 
parallelogram Cd = the area of Cc'd'e'D. In other words, the area 
cut olf is exactly equal to the area added. 

If now the distances AB, BC, CD, DE, etc., along the abscissa 
line be divided into equal portions representing one year each, 
then vertical lines drawn from the centre of each of these spaces 
will give the central population for each year of age.* 

The accuracy of the curve is confirmed by ascertaining that the 
sum of the ordinates draAvn from the base line within each space 
to the curved line bounding the space above is equal to the area of 
the parallelogram drawn on the same base. Thus in Fig. 39 
(7f?= 64712 = the sum of the five ordinates, 13420 + 13220 + 
13000+ 12710 + 12372.+ 

This method is not only very accurate, but it serves furthermore 
to remove the exaggerated oscillations occurring in figures on a 
small scale. The tracing of the curves being effected by a purely 
graphical process, difi"erent draughtsmen may arrive at slightly 
divergent results. It is, however, impossible that any material 
discrepancy can thus arise if due care is exercised, and if the rules 
set forth above are rigidly adhered to. 

Exactly the same method is pursued for the deaths occurring at 
each group of ages as that just described for population. The 
results are shown graphically in Figs. 39 and 40. The following 



* In the diagram, for the sake of clearness, the divisions for single years 
are not shown. In practice it is best done by means of Layton's actuarial 
paper, which is subdivided into accurately ruled small squares, thus enabling 
correct measurement to be made of the perpendiculars representing the number 
living or the number of deaths at the centre of each year. 

t It is not essential that in every case the sum of the ordinates shall 
exactly equal the area of the corresponding parallelogram. Occasionally it 
may be necessary to compensate for excess or deficiency in the neighbouring 
part of the curve. This is only exceptionally required in order to obtain a 
good curve. 



LIFE-TABLES. 



2G9 



is a sample of some of the population and death-groups before and 
after distribution by the graphic method. 

Total Number of Lives at Risk axd Deaths for each 
Year of Age. 



MALES. 


Age. 


Population. 


Deaths. 












In Original 


Distributed. 


In Original 


Distributed. 




Groups. 


1 


Groups. 




5 




14040 




100 


6 




13970 




78 


7 


69236 


13870 


333 


62 


8 




13740 




51-5 


9 




13616 




41-5 


10 




13420 




32-2 


11 




13220 




27-2 


12 


64712 


13000 


149 


26-2 


13 




12710 




27-4 


14 




12362 




36-0 


65 




2520 




IIS'5 


66 




2400 




123- 


67 




2250 




127-5 , 


68 




2110 




129- 


69 


19187 


1980 


1235 


129-5 


70 




1850 




129-2 


71 




1700 




128- 


72 




1580 




124- 


73 




1470 




116- 


74 




1327 




110-3 


95 




9 




3- 


96 


18 


5 


7 


2 


97 




2 




1 


98 




1 




1 


99 




1 







Population aged 0-5. The graphic method just described gives 
accurate results for the greater part of life. The first five years 
of life, however, give special difficulty whatever method of calcu- 
lating the central population of each of these years is adopted. 
This is inseparable from the defective character of the data for 
these years, the ages of young children being often inaccurately 



270 VITAL STATISTICS. 

stated in the census returns. Although the number of children 
at each year of age under 5 can be ascertained from the census 
returns, these numbers are untrustworthy. The total number 
aged 0-5 may be accepted as accurate, but the distribution of this 
total at each age under 5 must be found by an independent 
method. One of the following two methods may be adopted, 
preferably the latter if the data are available : — 

(a) The population under 1 year of age in any year may be 
taken as equal to the births from July 1st to December 31st of 
the preceding year plus the births from January 1st to June 30th 
in the same year, and minus the deaths under 1 year of age during 
the same half-year. Similarly the population under 1 year of age 
for the ten years 1881-90 may be taken to be equal to the total 
births from July 1st, 1880, to June 30th, 1890, mmus the number 
of deaths under 1 year of age in the ten years 1881-90. 

Thus, having ascertained the total male births from July 1st, 
1880, to June 30th, 1890, and subtracted from the result the total 
number of deaths of males under 1 year of age in the ten years 
1881-90, we obtain the population out of which the deaths at the 
age 1-2 occur during the same period. Subtracting the deaths at 
the age 1-2 we obtain the number out of Avhich the deaths at the 
age 2-3 occur ; subtracting these we obtain the population out of 
which the deaths at the age 3-4 occur ; and subtracting these we 
obtain the population out of which the deaths 4-5 occur. 

The sum of the five amounts thus obtained gives 76,627, which 
is the aggregate population at the commencement of the first five 
years of life. But when estimated from the census returns it is 
71,374, the difference being accounted for by migration. Hence 
these five amounts must each be reduced in the proportion of 
71374 
76627' 

Having obtained by this means the corrected population at the 
beginning of each of the first five years of life, we next proceed 
to obtain the mean population, which for each of these years 
except the first may be taken as the geometrical mean between the 
population at the beginning of the year {l^) and at its end (lx+\)- 
In other words the logarithms of the population at the beginning 
and end of the year are in arithmetical progression. The mean 
populations thus ascertained are 14,001 (1-2), 13,405 (2-3), 
13,135 (3-4), and 13,580 (4-5). 

The sum of these populations subtracted from 71,374 gives 
17,253 as the mean population of the first year of life. 



LIFE-TABLES. 271 

(b) The following is a somewhat more accurate method of obtain- 
ing the population aged 0-5, and where the necessary data are 
obtainable should be used. For the description of it I am indebted 
to Dr. Hay ward. 

To find the true mean numbers livincj and the values of j^x f^^' ^^^^ fi^^^ 
five years of life. 

For the ten years 1881-90 the data required are : 

(1) The true mean numbers living for each sex at the age-jjeriod 0-5 
calculated by the method previously described (or by the method to be 
descril)ed in the succeeding chapter). 

(2) The numbers of births, males and females, for each of the years 
1876-90. 

(3) The numbers of deaths for each sex. 

(a) At age 0-1 for the years 1877-90. 
{b) „ 1-2 „ „ 1878-90. 
{c) „ 2-3 „ „ 1879-90. 
(d) „ 3-4 „ „ 1880-90. 

I. For the mean annual number at birth in the ten years there must 
be taken 

^ births in 1880 + all births in 1881-89 + ^ births in 1890 
10 

II. For the mean annual number at 1 year of age. 

h births in 1879 -hall births in 1880-88 + ^ births in 1889 

less the number of deaths under 1 year of agein 1880-89 

10 

III. For the mean annual number at 2 years of age. 

i births in 1878 -hall births in 1879-87 -f-i births in 1888 
fess deaths under 1 year in 1879-88 

and deaths 1-2 years in 1880-89 

10 

IV. For the mean annual number at 3 years of age. 

^ births in 1877 -fall births in 1878-86 4- 1 births in 1887 
less deaths imder 1 year in 1878-87 
and „ 1-2 years in 1879-88 

„ 2-3 „ 1880-89 

10 

V. For the mean annual number at 4 years of age. 

I births in 1876-1- all births in 1877-85 -l-| births in 1886 
fess deaths under 1 year in 1877-86 
and „ 1-2 years^ in 1878-87 
„ „ 2-3 „ 1879-88 

, „ „ 3-4 „ 1880-89 

10 



272 VITAL STATISTICS. 

Five numbers ai'e thus obtained wbicb we may call 

a, h, c, d, e, calling the total "iV," 
a + b + c + d + e = N. 

It must be carefully noted that these numbers give not the population 
numbers at all ages from 0-1, from 1-2, etc., but the numbers actually 
starting at birth, at 1 year of age, etc. 

Now the true mean number living at the age-period 0-5 (which we 
may call G) which we have already calculated from the census enumera- 
tions, gives the total population at all ages from birth to age 5, and 
represents the total iV after half a year's mortality, as well as altered by 
migration. 

In order to make G correspond with iV, G must be carried hack half a. 
year by restoring the numbers of those who have died in the first half 
of the years of life. 

In the first year of life much more than half the mortality occurs in 
the first half of the year. For the other years the mortality may be 
considered to be evenly distributed. 

Therefore (7 + mean annual number of those dying under 6 months 

£ , mean annual number of deaths at ages 1-2, 2-3, 3-4. 4-5 
of ageH '■ 2 ! ! 

will give a value which we may call " T." 

The difference of T from N will represent the alterations due to 
migration. 

In order to eliminate these differences the total T must be divided 
up proportionately to the numbers a, b, c, d, e, which together give the 
total N. Thus— 



a 


N: 


:Po 


T 


b 


N: 


•.p. 


T 


c 


N: 


:Po 


T 


d 


n: 


:p. 


T 


e 


N: 


:p. 


T 



We shall thus obtain a series of five numbers which we may call 
Voi V\i V2-I P-ii l^ii representing the true mean annual number living 
at birth, at age 1, and age 2, etc. From these numbers the 2^x values 
for the first five years of life can be readily calculated. Thus — 

-P n - «o _ p 

— -t n 



Pi-di 
Pi 

P2 
Ps-ds p 

rl. 

= P. 



-Pi 
-P.. 



P^-d^ 



P 



LIFE-TABLES. 273 

Since tlie chance of living \ _ number livin g at end of year 

one year J number living at beginning of year 

and PQ = niean annual number at birtli, and fZQ = mean annual number 

P —d 
dying from age to age 1, it is obvious that the fraction -5- — 5 repre- 

sents the chance of living one year from birth, etc. 

This method of calculation i8, of course, lialjle to the fallacy that 
the migration of children under 5 years may not be exacth' 25i'opor- 
tionate for each of the first 5 years of life, but it at least gives more 
rational results than would be obtained by working from the obviously 
erroneous numbers of the census enumerations for these years. 

Const nirfion of the life-tahle. The number of lives at risk at 
each age, and tlie number of deaths at the corresponding ages 
and during the period with which the life-table deals being 
known, we obtain by division m.^ = the rate of mortality per 
unit of population, better known to actuaries as the central death- 
rate, because it represents the rate at which people are dying in 
the centre of a given year. 

From the m^ column, the probability tliat a person at each 
age Avill survive one full year {p,.,) can be obtained. 

The probability of living ) _ number of survivors at end of year_ 



through one year j number living at beginning of year' 
and we have already shown that 

_ 2 - 9»^ 



274 



YITAL STATISTICS. 



Probability op Life at 
Number op Survivors 
Number Born. 



EACH Age, and 
OUT OP a given 





The Probability 

of Living Cue 

Year. 


Number of Sur- 
vivors at each 
Year of Age out 




of 100,000 at 


Age. 


Px 


Birth. 


Males. 


Males. 





•84608 


100000 


1 


•93392 


84999 


2 


•97538 


79380 


3 


•98144 


77425 


4 


•98863 


75987 


5 


•99290 


75125 


6 


•99445 


74590 


7 


•99554 


74176 


8 


•99626 


73845 


9 


•99696 


73569 


95 


•63636 


"'l35 


96 


•66666 


86 


97 


•60000 


57 


98 


•60000 


34 


99 


•60000 


20 


100 




12 


101 




8 


102 




6 


103 




4 


104 




2 


105 








Thus 51,195 
43,315 



X •84608 = 43,315 

X ^93392 = 40,452, and so on. 



The p^ column calcu- 
lated from m^ for each 
age having been thus 
obtained separately for 
the two sexes, we can 
now build up the life- 
table step by step.* It 
is usual to start with 
100,000 children at 
birth. In Brighton dur- 
ing the ten years 1881- 
90, the births of male 
and female children were 
in the proportion of 
51,195 to 48,805, mak- 
ing 100,000 of both 
sexes. The numbers 
51,195 and 48,805 are, 
therefore, taken as the 
number at age in the 
l_^ column of the Brighton 
life-table. 

Starting with 51,195 
male infants at birth, the 
number living at the end 
of one year is obtained by 
multiplying this number 
by the probability of 
surviving to the end of 
the first year. 



In order to obtain the mean expectation of life for each 
individual, it Avill evidently be necessary to ascertain the total 
number of years lived by the individuals under consideration, and 
divide the sum by the number of individuals living this total 
number of years. The l^ column in the table of Avhich a portion is 
reprinted below (p. 275) gives the necessary data for this calculation. 

Thus the 43,315 males surviving to the end of the first year of 
life out of 51,195 born Avill have each lived a complete year in 

* For a shorter method of obtaining |),, see p. 260. 



LIFE-TABLES. 



275 



the first year, or among tlieni 43,3L5 years. Similarly 40,452 
males will live another complete year each in the second year, or 
among them a further 40,452 complete years; similarly 39,456 
complete years of life will l)e lived in the third year ; 38,723 in 
the fourth year, and so on, until the males started with Ijecome 
extinct at the af'e of 105. 



Brighton Life-Table, 

(Based on the Mortality of the Ten Years, 1881-90.) 

MALES. 



Age. 


Dying in each 
Year of Age, 
0-1, 1-2, etc. 


Born, and Surviving 
at eacli Age. 


Sum of the Number 

Living, or Years 

of Life lived at each 

Age x+\ and upwards 

to the last Age in 

the Table. 


Mean after Life- 
time (Expectation 
of Life) at each 
Age. 


X 


d^ 


i. 


■^'.r-l-i 


^°x 





7880 


51195 


2206174 


43-59 


1 


2863 


43315 


2162859 


50-43 


2 


996 


40452 


2122407 


52-96 


3 


733 


39456 


2082951 


53-29 


4 


440 


38723 


2044228 


53-29 


.5 


272 


38283 


2005945 


52-87 


6 


211 


38011 


1967934 


52-27 


7 


169 


37800 


1930134 


51-56 


8 


141 


37631 


1892503 


50-78 


9 


114 


37490 


1855013 


49-98 


10 


90 


37376 


1817637 


49-12 


11 


77 


37286 


17803-1 


48-14 


12 


75 


37209 


1743142 


47-35 


13 


80 


37134 


1706008 


46-44 


14 


108 


37054 


1668954 


45-54 


95 


25 


"69 


""l'l6 


i-68 


96 


15 


44 


72 


1-64 


97 


12 


29 


43 


1-48 


98 


7 


17 


26 


1-53 


99 


4 


10 


16 


1-60 


100 


2 


6 


10 


1-66 


101 


1 


4 


6 


1-50 


102 


1 


3 


3 


1-00 


103 


1 


2 


1 


-50 


104 





1 







105 












276 A'lTAL STATISTICS. 

It is evident, therefore, that the total number of complete years 
liveil by the 51,195 males started with at birth will be -1:3,315 + 

40,452 + 39,456 + 38,723+ 1 = 2,206,174 years. 

As tliis number of years is lived by 51,195 males, the number of 
complete years lived by each male 

2,206,174 ,0^0 
= -5M95- = ^^-^^^'^^^'^- 

This result is known as the curtate expectation of life 

We have, in the above remarks, confined our attention to the 
complete years of life, and have not taken into account that portion 
of lifetime lived by each person in the year of his death. In some 
instances this may only be a feAv days, in others nearly an entire 
year ; but it may be assumed with a fair degree of accuracy, taking 
one person with another, that the duration of life in the year of 
death will be half a year. 

If Ave add this half-year to the curtate expectation of life, the 
Complete Expectation of Life is obtained. 

Thus the complete expectation for males at birth = 43 09 + 0"5 = 
43-59 years; at the age of 10 years = 48*62 + 0"5 = 49'12 years. 
This method is accurate for most ages, but for the first year 0'5 
is too much. 

In the above specimens of the life-table only the complete 
expectation of life is printed. 

The headings given in the extract from the Brighton Life-Table 
on p. 275 are 

- (7,, 7„ 37^^ J, and e°,, 

I give a sample of two other life-tables, Avliich will throw light 
on some further points connected AA'ith a life-table. 



LIFE-TABLES. 



277 



Life-Table for England and Wales, based on the Mortality 
IN the Ten Years 1881-90. 



MALES. 


Age. 


Dying in each 
Yeai- of Age. 


Born and Sur- 
viving at each 
Age.* 


Population, or 
Years of Life 
Lived, in each 
Year of Age. 


Population, or 
Years of Life 
Lived, in and 
above each 
Year of Age. 


Expectation of 
Life at each 

Age., 


a; 


d^ 


Ix 


Px 


Qx 


Ex 


95 


162 


383 


302 


658 


1-72 


96 


99 


221 


171 


356 


1-61 


97 


58 


122 


93 


185 


1-51 


98 


32 


64 


48 


91 


1-42 


99 


17 


32 


24 


43 


1-33 


100 


8 


15 


11 


19 


1-24 


101 


4 


/ 


5 


8 


1-13 


102 


2 


3 


2 


3 


0-98 


103 


1 


1 


1 


I 


0-69 



Institute of Actuaries H.'*^ t (Healthy Males) Life-Table. 



Age. 


Number 
Living. 


Number 
Dying. 


Probability 

of Living 

1 year. 


^Ix+l 


^x 


hdj:+lx+\ = 
W'Jv+^x+V) 


2L, 
-T 


e°.r 


X 


h- 


d.,. 


V.V 






= L, 






85 


54 


11 


•796 


166 


3-07 


48-5 


193 


3-57 


8ti 


43 


9 


•791 


123 


2-86 


38-5 


144-5 


3^36 


87 


34 


8 


•764 


89 


2^62 


30 


106 


3T2 


88 


26 


6 


•769 


63 


2^42 


23 


76 


2 "92 


89 


20 


5 


•750 


43 


2^15 


17-5 


53 


2^65 


90 


15 


4 


•733 


28 


1'87 


13 


35-5 


2^37 


91 


11 


3 


•727 


17 


r55 


9^5 


22-5 


2-0.-. 


92 


S 


3 


■6-25 


9 


1-13 


6-5 


13 


1-63 


93 


5 


2 


•600 


4 


•80 


4 


6-5 


1-30 


94 


3 


2 


■334 


1 


■33 


2 


2-5 


•83 


95 


1 


1 


■000 







•5 


•5 


•50 



* Out of 509,180 started with at birth. 

t Taken from an Elementary Lecture on the Theory of Life Assurance, by W. J. H. 
Whitiall, P.I.A. (Layton). 



278 VITAL STATISTICS. 

In the second table a distinction is made between the curtate 
expectation of life (e^;), obtained by dividing the sum of those 
living at all higher ages by the number living at the beginning of 
any year of life, and the complete expectation of life, obtained by 
dividing the sum of the mean population at the same and all 
higher ages by the number living at the beginning of any year of 
life. V7 

Thus e.^ = :^\and 

e x = — ^. 

1 

Lx in the second table = Px in the first, 
J- x 11 )) = tij; 11 11 tind 

^ -r 11 11 = -t^x 11 11 

while -—— — = e°x = complete expectation of life. 

Ijx "X 

' The two tables may be utilized for a study of the principles 
underlying the construction of a life-table and of its applications. 
In the first table 383 men aged 95, and in the second 54 aged 85, 
are observed until death. These ages are chosen for the sake of 
brevity, but the principles involved are exactly the same as if the 
life-table had commenced at birth. The relation between the 
curtate and the complete expectation of life is clearly seen in 
the second table. Thus — 

166 o.n»7 

ho 54 



166 
54 



85 --^+¥ = 3-57 years; 



OJ'<s5 = -5j = 3-57 „ 

It is important to remember that the life-table represents a 
stationary population. A certain nimiber are started with at 
birth and traced through life according to the mortality experience 
of a given period of years ; but at every age, as deaths occur and 
the remainder pass on to the next year of life, their places are 
assumed to be taken by an equal number of the same age. Thus 
the 54 aged 85 in the second table become 43 aged 86, and their 
places are taken by another 54 who concurrently attain the age 
of 85. 



CHAPTER XXIII. 

ABBREVIATED OR "SHORT" METHODS OF CON- 
STRUCTING LOCAL LIFE-TABLES. 

FOR the following description I am indebted to Dr. Hayward, 
whose life-table for the urban district of Haydock, Lanca- 
shire, comprises what is, so far as I know, the best description of 
the construction of a life-table by the analytical method, and 
contains a number of novel suggestions and practical discoveries, 
which are embodied in the following descrijjtion : — 

The labour involved in constructing a complete or " extended " life- 
table, that is, calculating the chance of survival (px) and the expecta- 
tion of life (Ex) for every single year of life, even when simplified by 
the " graphic " method described in the preceding pages will be so 
considerable as to deter, perhaps, the majority of medical officers of 
health from undertaking it. 

In view, therefore, of the gi^at desiral)ility that every connnunity 
should possess the advantage of having available the only true measure 
of its vitality, it is of importance to ascertain whether by some simpler 
and shorter method, an approximation to the truth, sufficiently near 
for all practical purjjoses, cail be attained. 

Up to a certain point exactly the same work nnist be done for a 
short life-table as for a comjilete one. 

(1) The true mean total population for the decennial period most 
nearly corresponding to the interval l^etween two successive censuses 
must be calculated, corrections having been made, if necessary, in the 
census enumerations for public institutions, etc. 

(2) This total must then be divided up proportionately, so as to 
obtain the true mean numbers living in each of the age and sex-groups 
usually employed in classifying population, three quin(piennial age 
intervals being first taken, 0-5, 5-10, and 10-15, and afterwards 
decennial intervals to age 95. 

(3) The deaths must next be most carefully enumerated and 
classified into groups similar to those already ado])ted for the popula- 
tion, especial care being taken to include all those deaths properly 
Ijelonging to the district, but occurring outside it, as well as to exchule 
such deaths as may fairly be omitted as belonging to other districts, it 

279 



280 VITAL STATISTICS. 

being borne in mind that an error of one in tlie deaths will have a 
many times greater effect in vitiating tlie calculations than an error 
of ten in the ijopulation. 

(4) Separate calculations must then be made for each of the first 
five years of life by the method already explained. There is no short 
method for these years. If a simple calculation be attempted for 
this age-period based on the total population and total deaths at 
the age-period 0-5, the mean value of ih will be much too small, the 
Ix number for age 5 will be correspondingly diminished, and there- 
fore the Ex values at ages and 5 will greatly err in the direction of 
deficiency. 

To find the true mean population of a district for the ten calendar years 
most nearly corresponding to the interval between two successive censuses. 

The simple and obvious method of taking as the mean population of 
a district for ten years (say 1881-90) the arithmetical mean of the two census 
enumerations of 1881 and 1891 is unfortunately rendered erroneous by two 
reasons : — 

(1) On the assumption of a constant ratio of increase or deci'ease, the 
arithmetical mean nuist necessarily be greater than the true mean. 

(2) The intercensal period is later by the fourth part of a year, both 
at its beginning and ending, than the ten calendar years most nearly 
corresponding. 

If P be the population at the earlier census (1881), and P' the population 
at the later census (1891), then the rate of increase or decrease per unit or 

"11"=^- or P' = EP. 

The true mean population for 1881-90 may be found by dividing the 

PP + P^ 
arithmetical mean, that is, — -; by the factor 

R^'o x{R + l)x Hyp, log. E 

2(i2-l) 

In Part I. of the Supplement to the Fifty-fifth Annual Peport of the 
Registrar-General (pp. xliv. and xlv.) is given a most valuable table (called 
Table P), the result of an enormous amount of labour and calculation, 
by which the proper factor may be easily and simply calculated for any rate 
of increase or decrease. 

Taking the case of the population of Brighton, the total enumerated 
populations at the censuses of 1881 and 1891 were respectively 128,350 
and 141,970. 

Therefore 22 = ^-^^^^ = 1-1061161. 
128,350 

From "Table P" the factor of correction corresponding to jR= 11061161 
is found to be 1-003370 + ( 003408 - -003370) x •1161 = 1-003374. 
The true mean population, therefore, 

^i(128,350 + 141,97Q)^-^3^yQ..^ ^^^ 134 706)_ 
1-003374 
This differs by + 53 from the number obtained by the method previously 
desciibed on page 264. 



CONSTRUCTING LOCAL LIFE-TABLES. 281 

To find the (rue mean annual numbers living for each of the age and sex- 
groups info which the population is divided. 

Having given the total true mean population, this may be divided up 
into numbers corresponding to age and scx-groujis by the method of mean 
j)roj)ortions, which is based on the assumption that from one census to tlie 
next the proportions change uniformly. 

The steps of the calculation are as follows : — 

1. Calculate the proportions per million living in each of the age and 
sex-groups at each census. Thus, having given the facts — 

(a) That at the census of 1881, out of a total enumerated population for 
Brighton of 128,350, there were living 6158 males aged from 10 to 15. 

[b) That at the census of 1891, out of a total enumerated population of 
141,970, there were living 6829 males in the same age-group. We have 
the proportions : — 

6158: 128,350:: a;: 1,000,000, 

6158x1,000,000 .-o-Q.io 

X — = 4/9/8*19, 

128,350 

and 6829 : 141,970 : : x : 1,000,000, 

_6829x 1,000,000, 



141,970 



■ = 48101 71. 



2. Next find the proportion per million at the middle of the intercensal 
period, that is, five years after the earlier census. 

This is done by simply taking the arithmetical mean of the two propor- 
tions already found. 

Thus iZEiSLlSLtiMili .48039-95. 
2 

3. Take the difference between this last found value and the proportion at 
the earlier census. This will give the change of proportion in five years. 

Thus 48039-95 - 47978-19 = -t- 61 -76. 

4. Now we only want ^g of this last value for the change in proj)ortion 
for four and three-quarter years (corresponding to 50 of the total change in 
ten yeai's) 

Therefore, as the change in proportion has been in the direction of 
increase, the required mean proportion per million at the period of four and 
three-quarter years after the earlier census is found by subtracting v'^j of the 
change in five years from the value corresponding to the middle of the 
intercensal period. 

Thus 48039 95 ---''-^ = 48036 86. 
20 

If the change in proportion had been in the direction of decrease, the value 

^would have had to be added. 

20 

5. Finally, we have the ])roportion : — 

48036-86 : 1,000,000 : : tc : 134,706, 

48036-86x134,706 oat^.q 

x= ' = 6470 8. 

1,000,000 



282 VITAL STATISTICS. 

Supposing the work completed up to this point, and it is desired to take a 
"royal road " beyond, the short method hitherto usually employed has been 
that invented by the late Dr. W. Farr, and described by him twenty-three 
years ago in the Supplement to the Thirty-fifth Annual Report of the Registrar- 
General. 

The general principle of this method is to calculate from the numbers of 
population and deaths for a 5-yearly or 10-yearIy age-period, the mean value 
of 2)^ ; that is, the mean chance of surviving one year during the age-period, 
and then to use five or ten times this value, respectively, in calculating the. 
next stage in the l_^ column. 

In actual experience, as well as in the mathematical calculations of a 
complete life-table, it will, of course, be obvious that (after age 15) the 
chance of survival will be greater in the first year of the age-period, and 
less in the last year, than the mean value so found. 

A very simple calculation, involving only an elementary knowledge of 
the use of logarithms, suffices to determine these mean values of p^^ 

Having given the total mean number living, and the total number dying 
for a given age-period, the mean chance of living one year during the age- 
period is found by the fraction — 

population - ^ deaths _ 
population-)-^ deaths '^" 

Thus, having given the facts (1) that for the age-period 5-10, the mean 
annual number of males living in Brighton was 6923 "6, and (2) the mean 
annual number of deaths was 33 "3, 

_ 6923-6 -16-65 
^■^ 6923-6-M6-65 

and log. i?^. = log. 6906-95-log. 6940-25=:3-8392864- 3-8413752 = 1-9979112, 
therefore j;^ = -99520. 

This value only differs from the mean value of the separate p^^ values 
determined by the complete life-table by - -00002. 

Again having given the facts for the age-period 75-85, (1) that the mean 
annual number of males living = 714-3 ; (2) that the mean annual number 
of deaths = 94 -5, 

_ 7l4-3-47-25 _ 667-05 
■^•* 714-3 + 47-25 761-55 
2-8241584 



-2-8816984 



= 1-9424600= -87591. 



The mean value of the separate values of p^ for the age-period in the 
complete life-table = -85862, so that the value determined by the short 
method differs from this by + -01729. 

If the mean values of p>x for each of the decennial age-periods after age 
25, arrived at by the short method, be compared with the corresponding 
values determined in the complete life-table, it will be found that there are 
increasing differences in the direction of excess, as is shown in the following 
tabular statement : — • 



CONSTRUCTING LOCAL LIFE-TABLES. 



283 





Mean Values of p^ for Brighton 






(males). 




Age-periods. 


In the Extended ' By the Short 
Life-table. i Method. 


Differences. 


5-10 .... 


•99522 ! -99520 


- ^00002 


10-15 








•99769 -99770 


-f •ooooi 


15-25 








•99545 


•99544 


- •ooooi 


25-35 








•99226 


■99231 


-t- ^00005 


35-45 








•98693 


•98715 


+ -00022 


45-55 








•97872 


•97905 


+ •00033 


55-65 








•96719 


•96777 


+ ^00058 


65-75 








•93553 


•93764 


-f -00211 


75-85 








•85862 


•87591 


+ -01729 


85-95 








•71973 


•74121 


-f -02148 


95- 










•81333 





It will be noted that the value of 2\v for the age of 95 and upwards, as 
arrived at from the data, is much greater than that for the age-period 
85-95. 

This is a manifest anomaly, and cannot be in accordance with the actual 
facts. There is so much mis-statement of age, and the numbers dealt with 
are so small, that it is better, in order to obtain a working value of 2H5, to 
discard the actual data and to make a calculation based on the four or five 
preceding values of p^. 

The following method will give the required value : — 

Calculation of ^95 Fon Brighton (Male.s). 

Let the logarithms of the mean values of p^ for the four preceding 
decennial age-periods be set down in a colunm, and let their differences 
be taken until the third and last difference is jtained. Thus — 



log. ;755-c5 = 1-9857705 - 
log. i?63-75 = 1-9720363 ■ 
log. ;;r.5-^5 = 1-9424600 - 
log. ^;a5.95 = 1-8699353 



First Second Third 

Differences. Differences. Difference. 
-0137342 - -0158421 - -0271063 
■0295763- -0429484 
-0725247 



If these differences be continued downwards, it is obvious that a fifth 
equidistant term can be obtained. Thus — 

log. ^9:.= 1 8699353 - ( -0725247 + -04'29484 + -0271063) = 1 -7273559. 
Therefore pi^= •53377. 

From the series of mean values of p^ for the age-periods from age 5 
onwards, it is now possible to continue the calculations of Z^ from the 
Is value, already calculated in the complete life-table, and the results 
arrived at are as follows : — 



284 



VITAL STATISTICS. 



Values of E^. obtained for Brighton (Males) by Dr. Farr's 
"Short" Method, compared with the Corresponding Values in 
THE Extended Life-Table, denoted respectively by " B" and "A." 



Age 


B. 


A. 


Differences of B 


X. 






from A. 





43-84 


43-59 


+ -25 


5 


53-25 


.52-87 


+ -38 


10 


49-49 


49-12 


+ -37 


15 


45-03 


44-67 


+ -36 


25 


36 91 


36-51 


+ -40 


35 


29-46 


29-02 


+ -44 


45 


2-2-84 


22-36 


+ -48 


55 


17 05 


16-48 


+ -57 


65 


11-72 


10-96 


+ -76 


75 


7-80 


6-64 


+ 1-16 


85 


5-50 


3-33 


+ 2-17 


95 


5-00 


1-68 


+ 3-32 



This method, while at the earlier ages giving a moderately close 
approximation to the results of a complete life-table, can scarcely be 
considered at the later ages as entirely satisfactory. 

If we analyze the reasons for the discrepancies in the direction of 
excess of the values of Ex obtained, they are found to be twofold. 

(1) The progressively increasing values of p^ over the mean values 
of the complete life-table already demonstrated. The values of Ix are 
therefore increased, and the years of life calculated from Ix and 
lx-\-\Q are increased in greater proportion than Ix is increased. 

(2) But even if we were able to get the mean values of px by 
the short method to exactly correspond with those of the complete 
life-table, and, therefore, the values of Ix to be identical, the calculation 
of the years of life at 10-yearly intervals would give errors in excess 
over the sums of the sej^arate yearly values, and therefore the values 
of Ex would be too great. 

However, by a simple modification of Dr. Farr's short method, Dr. 
Hayward found that very close approximations to the true Ex values of 
a complete life-table can be obtained. His results were embodied, in 
the first instance, in the life-table for Haydock, and are reproduced 
here by his permission and assistance. 

Going back to the point at which we had the data, (1) the number 
of survivors at age five already calculated, (2) the mean values of 
Px for the various age-periods, the years of life lived in each decennial 
age-period were calculated by Dr. Farr's method thus : — 

^x + WiO xio=:years of life. 

To take a numerical example. Suppose that at age 75 we have 
survivors numbering 16,000, and that the mean value of px for the 
age-jDeriod 75-85 has been found to be -87055, then the number of 
survivors at age 85 will be 16,000 x (•87055)i''=4000, .and the years 

f ... -i, , 16,000 + 4000 ,^ inn AHA 

of lite will be — ^ x 10 = 100,000. 



CONSTEUCTING LOCAL LIFE-TABLES. 



285 



tivo stages instead of one, the 



Now if the calcuhition be made in 
result will come out as follows : — • 

(1) 16,000 X (-87055)5 = 8000; 

(2) 8000 X (-87055)5 = 4000, 

and the years of life = ( ^^^OO + ^^^O + 8Q00 + 4000 j ^ ^ ^ ^^^^^^^ 

Again, the calculation may be made in foicr stages : — 

(1) 16,000 X (•87055)2^=11,314; (2) 11,314 x (-87055)2^ = 8000; 

(3) 8000 x(.87055)2i = 5656; (4) 5656 x (-87055)2^ = 4000, 

and the years of life = 

/ 16,000 + 11,314 11,314 + 8000 8000 + 5656 5656 + 4000 \ 
V 2 2 2 2/ 

X 2.1 = 87,425. 

Similarly the calculation may be made in te7i stages, with the result 
of reducing the estimated years" of life to 86,701. 

It is thus obvious that l:)y the simple device of reducing the 
calculated years of life by increasing the number of stages in the 
calculation of Ix+io fi'om L-, the possibility is presented of obtaining 
values of Ej^ more nearly approaching the true values. 

Dr. Hayward has made it a matter of experiment to find the most 
simple and most accurate application of this idea. Startiiig again 
with the ^5 number in the complete life-table, and with the mean 
values of ^jjr calculated by the short method, the following rules have 
been adopted : — 

(1) For each of the decennial age-periods for age 15 to age 85 the 
calculation has been made in two stages. 

(2) For the age-period 85-95 four stages have been used. For most 
of the other Life-tables in which the method has been tried a more 
accurate result has been obtained by making the calculation of the 
age-period 75-85 also in four stages. 

(3) After age 95 the calculation has been made in yearly stages. 
The results obtained are shown in the following table : — 

Calculated Values of Ex for Brighton (Males), "C" com- 
pared WITH THE corresponding VaLUES "A" OF THE COMPLETE 

Life-table. 



. 

5 . 
10 . 
15 . 
25 . 
35 . 
45 . 
55 . 
65 . 
75 . 
85 . 
95 . 



c. 

43-53 

52-84 

49-07 

44-61 

36-46 

28-98 

22-30 

16-42 

10-93 

6-65 

3-40 

1-63 



A. 


Difference of C 




from A. 


43-59 


--06 


52-87 


-03 


4912 


-•05 


44-67 


-06 


36-51 


--05 


29-02 


--04 


22-36 


-•06 


16-48 


-06 


10-96 


-•03 


6-64 


+ -01 


3-33 


+ 07 


1-68 


-05 



286 VITAL STATISTICS. 

It is therefore evident that by this short and easy method values 
of Ex are to be obtained at decennial age-intervals api^roadiing the 
true values with remarkable exactitude. 

It must be carefully noted that this method does not give accurate 
values of Ex for the intermediate even ages, 20, 30, etc. The inter- 
mediate values of Ix+s obtained are of no use, except as helping to 
reckon the years of life lived in the interval between age x and age 
x + lO. 

From these decennial values of E^ it is possible to obtain the inter- 
mediate quinquennial values by a simple method of " interpolation." 

(1) Where there are four equidistant terms of a series to work with, 
as for instance Ej^^, E.^s, E^^, and E^r,,from ten times the sum of the tioo 
middle terms subtract the sum of all four terms, and divide the remainder 
by 16, the result is the centre term Eqq required. 

Thus E.r. = 10 (^^25 +-^35)- (^ 15 +^25 +-5 ^3 5 +-^45) . 

16 



'30- 



(2) Where at the top or bottom of the series there are only three 
terms to work with, together with a fourth term already interpolated 
by the preceding formula, to one-fourth of the sum of the two outside 
terms add one and a half times the inside term, and subtract from the sum 
the value of the term already interpolated. 

Thus ^90 = ^^^^^^ + li- ^85 -^80, 

and^2o = ^^^-±^ + l*-^25-^3o: 

These formulae are to be easily deduced from " Lagrange's Theorem." 

It is useless to attempt to obtain values of Ex at the intermediate 
even ages by taking the enumerated population and recorded deaths at 
5-yearly intervals, and calculating the px values from these numbers. 
The results are so uneven as to be quite unreliable. 

It is a Avork of considerable labour to interiJolate intermediate 
quinquennial values in the numbers of population and deaths by 
formuljB corresponding to those above given applied to the logarithms 
of the numbers representing population and deaths at age x and 
upwards, whereas by reserving the interpolation until the last stage 
in the Ex numbers, the labour is very much less, and the results equal 
in accuracy those already obtained for the odd ages. 

Those who may desire to have a more detailed explanation of this 
method, and to see its results as applied to other life-tables, may refer 
to Dr. Hay ward's paper " On Local Life-Tables by Short Methods," in 
Public Health, vol. x. no. x., July, 1898. 

History of Life-Tables. The earliest English Life-Table was con- 
structed by Halley, the English astronomer, in the second half of the 
seventeenth centurv. It was calculated on the deaths in the city of 



CONSTRUCTING LOCAL LIFE-TABLES. 287 

Breslau in the years 1687-1091. Males and females are not distinguished 
in it, nor in the Northampton and Carlisle Tables. 

De Moivre's hypothesis was suggested by Halley's Breslau Tables. 
He concluded that the hypothesis that out of eighty-six persons born 
one dies e\ery year till all are extinct, would very nearly represent the 
mortality of the greater part of life, and that in the calculation of 
annuities its errors would nearly comi^ensate one another. Tables 
formed on this hy^iothesis, as well as on the Northampton Table to be 
next considered, overstate the mortality of young adults. The con- 
sequence is, that in life assurances calculated on the results of De 
Moivre's and Price's Tables, the young are made to pay for the old, and 
injustice is done to those who insure com2)aratively early in life. 

The first life-table used for the purpose of determining the rate of 
premium to be ]\aid for life assurance was Dr. Price's Northampton 
Table, which was used by the Ecjuitable Office on its establishment in 
1762. Like Halley's Table, owing to the want of jiroper materials, the 
Northam2)ton Table was not constructed by a compai'ison of the 
deaths a)td the Uviiuj at each aye, but from the deaths alone. Tables con- 
structed on this latter plan are only correct when the population in 
which the deaths occur remains stationary ; i.e., when the births and 
deaths are equal in number, and there is no disturbing migration. 
Dr. Price Avas under the misapprehension that the population of 
Northampton was stationary, judging by the numljer of infantile 
baptisms. But at the time the data for this table were recorded, there 
were a large number of Baptists in Northampton, who repudiated 
infantile baptism. The consequence of this oversight was that Dr. 
Price assumed the mean duration of life to be twenty-four years, when 
it was really about thirty years. Unfortunately his table was made 
the basis for the government annuity schemes ; and the same error 
which gave the insurance offices one-third too high jsremiums induced 
the government to grant annuities by one-third too large for the price 
charged, resulting in a loss to the public funds of about two millions 
of money before the error was corrected. 

Dr. Price also constructed a correct life-table from the population 
and deaths in Sweden, "which was the first national life-table ever 
made, and redounds much more to his fame than the Northampton 
Table" (Farr). 

The Carlisle Table was formed by Mr. Milne, from the observations 
of Dr. Hey sham, upon the mortality of that town in the years 1779-89, 
and two enumerations of its population in 1779 and 1787. At the 
time it was constructed it showed results too favourable for the whole 
country ; but owing to the decrease of mortality which followed, it 
became more accurate. De Morgan gives the following expression, 
based on the Carlisle Table, as representing more nearly the mortality 
from the age of 15 to that of 65 than does De Moivre's hypothesis. 
Of every one hundred persons aged 15, one dies every year till the age 
of 65. Or if we take the mean after-lifetime, according to the Carlisle 



288 VITAL STATISTICS. 

Table, between the ages of 10 and 60, for rougli purposes it may be 
said : Of persons aged 10 years, the mean after-lifetime is 49 years, 
Avith a diminution of 7 years for every 10 years elapsed ; thus, of 
persons aged 20 years, the mean after-lifetime is 49-7 = 42 years ; at 
30 years of "age, 35 years, and so on. The mean after-lifetime, according 
to different life-tables, is shown in the table at p. 299. 

Details respecting the Amicable Society's Table and the Equitable 
Table, the latter of which gives the experience of the Equitable 
Society from 1762 to 1829, of 5000 lives ; the Government Tables, 
which give the experience of 22,000 government annuitants; or the 
Experience Table, based on the recorded experience of seventeen life 
offices and 83,905 lives, cannot be given here. We must pass on to 
Dr. Farr's Life-Tables, which are based on the census and death-returns 
of the whole of England and Wales, and not of insured and therefore 
selected lives like the preceding. 

English Life-Table, No. 1. Dr. Farr, believing that nothing short 
of a table based on the returns of the entire kingdom would be satis- 
factory, constructed his No. 1 Table, based on the census returns of 
1841 and the deaths of the same year (Bajistrar General's Fifth Eeport). 
Thinking, however, that the records of one years deaths might be open to 
challenge owing to the short time embraced in them, he constructed the 
English. Life-Table, No. 2, This is founded on the census enumera- 
tions of 1831 and 1841, and the deaths of seven years are taken ; viz., 
those in 1841 and the three previous and three subsequent veai's. It is 
thus based upon the recorded ages of 13,896,797 + 15,914,148 = 29,810,945 
persons, and on the registered deaths of 2,436,648 ]iersons. 

The difference between these two English Life-Tables, as shown by 
the number of survivors at various ages, and by the mean after-lifetime, 
is slight. 

The English Life-Table, No. 3, constructed by Dr. Farr, was based 
on the census enumerations of 1841 and 1851, and upon the 6,470,720 
deaths registered in the seventeen years 1838-54. 

For a detailed description of the methods of construction of this 
table, the reader is referred to the English Life-Table, by Dr. W. Farr : 
Longman and Co., 1864. 

The near agreement between the results obtained by these three 
English Life-Tables is very remarkable, and shows that, spite of annual 
liuctuations, there was a fairly stationary mortality during 1838-54, 
which, we may add, continued up to the year 1871. The latter fact led 
Dr. Farr to abandon his intention of constructing a fourth English 
Life-Table down to 1872. 

The Healthy Districts Life-Table was constructed by Dr. Farr on 
the basis of the mortality during the five years 1849-53, in sixty-three 
selected English districts Avhich showed, during the decennium 1841- 
50, a mean annual death-rate not exceeding 17 per 1000 persons living. 
As pointed out by Dr. Farr, it exjiresses "very accurately the actual 



CONSTRUCTING LOCAL LIFE-TABLES. 289 

(luratiou of life among the elevgy and other classes of the community 
living under favourable lircumstances." It represented also a standard 
oi healthiness already attained, and was therefore useful for purposes 
of comparison. This table is printed in the ThirUj-third Annual Report 
of the Rerjutrar-General. 

The Upper Class Experience Table was constructed by Mr. C. 
Ansell from data collected ))y him as to men of the up])er and pro- 
fessional classes, and given in his Statistics of Families in the Upper 
and Pwfcssional Classes, 

The Healthy Males Table of the Institute of Actuaries is based on 
the experience of the principal insurance offices in regard to insured, 
and therefore exceptionally healthy, lives. 

The Clerical Experience Table is based on data respecting over 
5000 clergymen living between 17G() and 1860. 

The English Life-Table by Dr. Ogle, published in the Supplement to 
the Thirtii-fifih Annual Report of the Registrar-General, deals with the 
national experience in the decennium 1871-80, and that by Dr. Tatham 
with that for 1881-90. 

The New Healthy Districts Life-Table, by Dr. Tatham, forms a 
valuable index of sanitary i)rogress in recent years. Thus whereas in 
1841-50, the period dealt with by Dr. Farr's Healthy Districts Life- 
Table, " less than 6 per cent, of the total population lived in districts 
the crude death-rates in which were below 17-5 i)er 1000 ; in 1881-90, 
on the other hand, no less than 25 per cent, of the population lived in 
districts the crude death-rates in which fell below 17-5 ])er 1000, and 
4.\ per cent, in districts the crude death-rates in which did not reach 
15-0 per 1000." There are differences of age and sex-constitution to 
be allowed for ; which has been done in the last decennial supplement, 
by obtaining death-rates in a standard population. When this has been 
done, it is found that al)out one-sixth of the entire population, or 
4,606,503 persons, had death-rates below 15 per 1000 in 1881-90. This 
new table is therefore calculated on 46 million years of life, a basis 
more than nine times as great as that of the older table. 



CHAPTEE XXIV. 

METHODS OF CALCULATING THE DUEATION 
OF LIFE. 

n^HE duration of life is the problem with which vital statistics 
X are largely occupied; while preventive medicine is largely 
concerned with endeavours towards the attainment of Isaiah's 
ideal (chap. Ixv. 20) : " There shall be no more thence an infant 
of days, nor an old man that hath not filled his days : for the 
child shall die an hundred years old." Although nothing is more 
uncertain than the duration of life, when the maxim is applied to 
the individual, there are, as Babbage has put it, " few things less 
subject to fluctuation than the duration of life in a multitude 
of individuals." It is on this principle that annuities and life 
assurance can be made the subject of definite and exact calcula- 
tions, the final results being found to vary within but narrow 
limits. 

Several tests are employed to measure the duration of human 
life, and we are concerned in this chapter to determine their 
precise value and the relationship existing between them. 

Those most commonly employed are : — 

(1) The mean age at death; 

(2) The probable duration of life ; 

(3) The mean duration of life ; 

(4) The expectation of life, or mean after-lifetime ; 

(5) The number living out of which one dies annually. 

In a life-table or normal population, when all the lives are 
included in the calculation, the mean age at death, the expectation 
of life, and the number out of which one dies annually, are 
numerically identical. The thorough comprehension of this point 
will go far towards elucidating the relationship between the five 
above means of testing the duration of life. 

290 



THE DUEATION OF LIFE. 291 

In the construction of the life-table we have seen (p. 274) that 
when the sum of the numbers living at all the ages higher than a 
given age x is taken, eacJi life is counted once for every complete 
year it survives after the age x. The sum total represents the 
total number of complete years of life lived by the persons who 
enter upon the year of life x. If this sum be divided by the 
number who, according to the life-table, enter upon this year 
of life, the quotient will be the individual expectation of life at 
the age x, so far as complete years of life are concerned. (If we 
add to this amount half a year as rej^resenting the average 
duration of existence during the ;f"' year of life for those who die 
during that year, we obtain the complete expectation of life.) 
But the above sum (of the numbers living at all the ages above x) 
is also the number constantly living in the place above the age x. 
Thus in the Brighton Life-Table out of 51,195 male children 
at birth, sixty -nine are left at the age of 95 years, and the sum of 
the number living at all higher ages is 44 + 29 -f 17 + 10 -f 6 

-t-44-3 + 2-Fl = 116 years. But ij^ = 1 -68 = the individual cur- 
•^ 69 

tate expectation at the age of 95. The number 116 also 

represents the sum of the number of males constantly living in 

Brighton at ages above 95 oi;t of 51,195 male children born, who 

have been traced through life in accordance with the mortality 

experience in 1881-90. In other words, it represents the entire 

population aged over 95. Inasmuch as these all die at this or 

some subsequent age, if we divide the entire population 116 by 

the number 69 who are living at the age 95, we obtain the 

number out of which one dies annually, which is identical with 

the expectation of life. 

In the preceding illustration it has been shown that the 
number out of which one dies annually and the expectation of 
life are identical for the age 95. It can similarly be shown that 
they are identical at birth or any subsequent age. 

At birth the mean age at death is also identical with the mean 
expectation of life, as may be ascertained by the somewhat 
laborious method of dividing the sum obtained by adding together 
the total ages of the dying in each year of life, and finding this 
sum by the total number of deaths. 

Thus in a stationary or life-table population the following 
represent identical quantities : — 



292 VITAL STATISTICS. 

Mean age at death of persons at all ages 
_ Sum of ages at death 
~ Total No. of deaths 
_ JS'iimher of population 

No. of deaths in one year 
= Mean duration of life 

or, jMean expectation of life )■ at birth. 

or, Mean after-lifetime 

In Dr. Farr's Life-Table population, the persons become reduced 
to one-half in 45 3'ears = tlie probable lifetime; the mean after- 
lifetime = 40*9 years, or very nearly 41 years; and this = the 
mean age at death. In such a life-table population to forty-one 
persons living there is one birth and one death annually ; the rate 
of mortality is one in forty-one ; and forty-one is the mean after- 
lifetime or expectation of life. 

Mean Age at Death = ?HBL4jlS514li^\ Thus, if five 
number of deaths 
persons die at the ages 10, 20, 30, 40, 50, their mean age at 

. ,, 10-^20 + 30-^-40 + 50 o^ , ., , 

death = = oO years ; and it a second group 

o 

of five die at the age of 25, 30, 45, 50, 70 respectively, their 

f ^ 4-1 -11 1 25 + 30 -F 45 + 50 + 70 ,, 

mean age at death Avill be = 44 years. 

o 

Assuming that these two groups of persons were exposed during 
life to similar influences, the question arises, Would the mean 
age at death of the two groups form a safe standard of com- 
parison between themi It should be noted, to begin with, that 
the number of persons in the instances quoted is very small, 
and cannot therefore form a trustAvorthy basis for comparison. 
But even if each group embraced a large number of persons, 
erroneous conclusions Avould certainly be drawn, as the age- 
constitution of the two groups is so difl'erent. In a normal or life- 
table population, the mean age at death is, as already seen, the 
same as the expectation of life at birth. But in a population 
like that of England and "Wales, where the births constantly 
exceed the deaths, and the population is an increasing one, the 
mean age at death is necessarily lowered by the large proportion 
of deaths of young children. On the other hand, when a high 
birth-rate continues for a series of years, there being added every 
year to the population more than are taken from it by death and 



TI[E DT'TJATIOX OV LIFE. 



29.3 



migration, there results an excessive proportion of persons between 
the ages of 5 and 55, during wliich period of life the death-rate 
is below the average death-rate for all ages. Consequently we 
liave the following facts for England and Wales in 1881-90 : — 





England and Wales. 


Males. 


Females. 


Persons. 


Mortality 

Mean Age at Death* .... 
Mean Expectation of Life at Birth 


1 in 49 
30-5 
437 


1 in 55 
33 9 

47-2 


Iin52 
32-1 
45-4 



* Calculated approximately by Dr. Hayward (Haydock Life-Table, p. 32). 

The proportional mortality, and the mean age at death, are seen 
to be lowered by the continued excess of births over deaths, and 
are not equal to the expectation of life, as they Avould be in a 
life-table population. 

In contrastimi different nations the mean age at death is a most 
fallacious test, owing to variations in birtli-rate and in migration 
of i)opulation. This is shown by the following table from Farr's 
Vital Statistics, p. 473 : — 





Mortality ; or, 
One Death 


Mean Age 
at Death. 


Mean After-life- 
time or Expecta- 
of Life. 


England (1841) . . j In 46 living 
France ,, . . ! ,, 42 ,, 
Sweden ,, . . ! ,, 41 ,, 


29 years 
34 ,, 
31 ,, 


41 years 
40 ,, ? , 
39 ,, 


Metropolis ,, . . 
Liverpool ,, . . 


„ 41 „ 
» 30 „ 


29 „ 
21 „ 


37 „ 
26 ,, 


Snrrey (extra-Metropolitan) 


,, 52 ,, 


34 ,, 


45 „ 



It will be observed that in England, where the mean age at 
death was loAvest of three countries in 1841, the mortality was 
also lowest, but the true expectation of life, as deduced from a 
life-table, Avas highest ; whereas if the mean age at death Avere 
a trustworthy test of the duration of life, a low mean age at 
death ought to be accompanied by a high mortality. 

It may be inferred from the above table that the mortality 
(number out of Avhich one death occurs), although it does not 
pretend to express the true mean expectation of life, gives a much 



294 VITAL STATISTICS. 

nearer ai-)proximation to it tliaii does the mean age at death. This 
will be at once seen if the mortality and expectation of life 
columns in the preceding table be arranged side by side, for they 
coincide in position in every instance, unlike the mean age at 
death, which gives very variable indications. 

(1) In contrasting the same country at different periods, similar 
fallacies may arise. Thus 49 per cent, of the total population was 
under tAventjr in England in 1821, but in 1891 only 45 per cent., 
which would have considerable effect on the mean age at death. 

(2) We have seen that tirha?i poindations consist in a much 
larger proportion of persons under forty than do rural populations. 
Similar differences may exist between the several districts of large 
cities, and correction for different age-constitution of populations 
may sometimes reverse the apparent position of the populations 
under comparison. 

(3) In the comparison of different classes of society, and those 
engaged in different occup)aHo7is, serious errors have arisen by the 
use of this test to determine their relative vitality. It Avould be 
absurd, for instance, to draw any inferences from a comparison of 
the mean ages at death of bishops and curates, as men do not 
usually become bishops till they have passed the middle joeriod of 
life. Similarly in comparing the gentry Avith tradesmen. Many 
gentry are retired tradesmen, and their mean age at death is 
therefore higher than that of tradesmen. A Socialist leader in 
1890 stated that the mean age at death of Avorkmen Avas 29-30 
years, of the Avell-to-do classes 55-60 years. This statement does 
not shed any light on the relative vitality of the tAA^o classes under 
comparison. It simply shows that the Trade Union Societies, 
from AAdiich some of the above figures Avere deriA^ed, consisted 
largely of young men, Avhose age at d.eath, if they died at all, must 
necessariljr be loAver than that of the Avell-to-do classes, consisting 
as they do in a large measure of persons retired from active Avork. 

The acceptance of the mean age at death as a test of the 
duration of life is a fragment of the error involved in the con- 
struction of a life-table from the deaths alone, as in Dr. Price's 
Northampton Table (see p. 287). 

Effect of Birth-rate upon the Mean Age at Death. We 

have already seen that in a stationary population unaffected by 
migration, in AA'hich the births equal the number of deaths, the 
expectation of life at l)irth is identical Avith the mean age at death, 
and Avitli the number of the population out of Avliich one death 



TTIE DURATION OF LIFE. 



295 



annually occurs. Inasnuicli as the hirths and deatlis are equal in 
nunil)er, the mean age at death is also equal to the number out of 
whicli one annual hirth occurs. In a non-stationary po^julatiou 
the state of matters is altogether different. 

The late Sir B. W. Richardson claimed for the inhabitants of 
his " Hygeiopolis " that their death-rate would be reduced to five 
jier 1000. It was soon afterwards asserted in the 'Times that this 
Avould imply a mean duration of life (using the term in the sense 
of mean age at death) of 200 years, and that a fortiori Sir B. W. 
Richardson's anticipations were absurd. It is only, however, where 
the i)opulation is stationary that the mean age at death would be 
200 years ; and under existing conditions the above anticipation 
was not quite so absurd as it appeared. 

Dr. B)-istowe, in the St. Tliomas's Hospital Report for 1876, 
worked out the influence of variations in the liirth and death-rate 
on the mean age at death. He assumed the simplest .condition of 
things, viz., that in each case the birth-rate and deatli-rate continue 
uniform from year to year ; that no immigration or emigi-ation 
occurs ; and that every individual born into the population attains 
the mean age, or, in other words, all the inhabitants die at the 
same age. Under these conditions, where the births exceed the 
deaths, the population, births and deatlis, all increase from year to 
year by geometrical progression. 

Let number of population from which we start =1, and h = 
birth-rate, and d = death-rate of this unit, and r = its annual 
increase ; i.e., r = h- d. 

Then the following three series will represent the annual groAvth 
of the population, of the births, and of the deaths respectively. 





Population. 


Births. 


Deaths. 


1st Year 

2nd ,, 

3rd „ . . . 

4th ,, . . . 

7tth ,, 


1 
(1+r) 
{l+rf 
(\+rf 

(1 +,.)«-! 


b 

b{\+r) 
b{l + rf 
b{l+rf 

J (1 + ,.)«-! 


d 

d(\+r) 
d{l+rf 
d{\+rf 
d{\ + r)''-^ 



According to the hypothesis with which we started, all the 
jH'rsons born in any one year die together in the course of some 
subsequent year, and the number of that year, reckoning from the 
time of births, is the mean age at death. It is evident, there- 
fore, that if we can ascertain the number of that term in which 



296 VITAL STATISTICS. 

d(l +ry"^ = b, the value of the index n-l will represent the mean 
age at death. Let x = the value of the unknown index. 
^ JSTow from d{l +ry = b, we obtain 

and taking the log. of each side of this equation, 

X log. (1 + r) = log. b - log. d, 

_ log- ^ ~ log- "^ 
log. (1+r) 

from which equation the value of x is easily determined. 

The assumptions made as to the constitution of the population 
and their uniform age at death are absent in experience ; and the 
formula cannot be applied under the actual conditions of any 
known community with advantage. It is useful, hoAvever, as indi- 
cating that a high death-rate is not incompatible with longevity ; 
and that a low death-rate, apart from any consideration of the 
birth-rate, does not necessarily imply a long-lived population. 

Mean Length of Life. The term " mean length of life " has 
been employed by Professor Corfield to indicate the figure obtained 
by the application of the preceding formula to the birth-rate and 
death-rate of the parish of St. George, Hanover Square, London. 
The formula shows a much more favourable result for this parish 
than for many other parts of London. For the reasons given 
above this test cannot be considered to possess any value. The 
birth-rate can only influence the death-rate by altering the pro- 
portionate number of persons living at different ages, and therefore 
exposed to the varying chances of death associated with these 
ages. If there is a large excess of persons living at ages under 5, 
the "mean length of life" will be low, because about 6 per cent, 
of these children will die. If there happen to be a large excess 
of persons living at the opposite extreme of age, the " mean length 
of life " will be high. Consequently there are only two means of 
accurate comparison of the vital statistics of different populations. 
(a) The best is the comparison of expectations of life derived from 
a life-table, (b) The next best is the statement of the deaths at 
each age-group in proportion to the number living at the corres- 
ponding age-group. 

Dr. Eumsey urged that returns should be made of the mean 

- ., ,. . sum of ages of population at census 

age of the living = ^— ; ^ , — -. as a cor- 

number of population 



THE DURATION OF LIFE. 297 

rective of the fallacies connected with the mean age at death. He 
adds it is now " clear that the average duration of the lives of those 
Avho die in any place or country does not imply the average age of 
those who live there, any more than it means their average ' ex- 
pectation of life.' " He gives the following example, taken from 
the experience of the metropolis a quarter of a centiiry before 
the date of his remarks : " Paradoxical as it may seem to the 
uninitiated, one out of forty-one may die annually, the mean age 
at death may be twenty-nine, the mean age of the living may be 
twenty-six, and the mean expectation of life may be thirty-seven, 
in the same population at the same time." {Essays on some 
Fallacies of Stafisties, 1875, p. 211.) Sir E. Chadwick found 
that in fairly healthy districts the mean age of the living was to 
the mean age at death as about 3 to 4, while in insanitary 
districts with shifting and increasing populations the line of 
vitality was higher than that of mortality. But this is due to 
the fact that under insanitary conditions a high mortality spends 
itself chiefly among young children, and, in addition, there are 
always crowds of young and healthy persons ready to immigrate 
from country to town, thus lowering the mean age of the town 
populations, among whom insanitary conditions are especially rife. 
On the whole, therefore, the mean age of the living as a test of 
the duration of life is as untrustworthy as is the mean age of 
the dying. 

The Probable Duration of Life (also called equation of life, 
or vie 2-»'o()ahle) is a term used to signify the age at which any 
number of children born into the world will be reduced to one- 
half, so that there are equal chances of their dying before and 
after that age. The name is unfortunate, as every possible 
duration of life has a probability which may be determined, and 
is therefore mathematically a "probable lifetime." Using the 
term in its limited sense, the English experience in 1838-54 gave 
a probable lifetime for males at birth of 44-45 years, while 
according to the experience of 1881-90 it was 51-52 years. 

De Moivre's Hypothesis. This assumed that the decrements of 
population are in arithmetical progression, and that of every 
eighty-six persons born, one would die uniformly every year until 
all were extinct. Such an assumption was convenient in the 
calculation of annuity tables, before accurate life-tables were 
constructed. According to this hypothesis there is no such function 
as the probable duration of life, the proliability of death in any 
year being as great as in any other. It confessedly errs greatly at 



298 VITAL STATISTICS. 

the beginning and end of life, and is only a very rough approxima- 
tion to the truth for the middle period of life. 

The Mean Duration of Life, or vie vwyenne, is a term which 
has unfortunately been employed with different significations. 

The following table of the diverse mathematical expressions to 
which the name vie moyenne has been given is taken from Bertillon 
{op. cit. p. 75) : — 

Vie Moyenne, France, 1840-49. 

Years. 

True vie moyenne (expectation of life) .... 40-05 

Mean age of persons enumerated at census . . . 30-92 

„ deceased persons 35-66 

Number of population out of wliicli one birth occurs . 38-00 

„ „ „ „ death „ . 43-50 

Mean between the two preceding values (Price's formula) 40-75 

Vie 'probable, according to life-table 43-30 

„ „ „ death-returns .... 33-50 

In a stationary population, undisturbed by migration or other 
causes, expectation of life and the mean age at death are, as we 
have already seen, identical. In populations as ordinarily con- 
stituted the term " mean duration of life " should not be employed 
except as synonymous with expectation of life or mean after- 
lifetime ; and having regard to its loose application it would be 
preferable to drop it altogether. B}'' some actuaries the term is 
employed somewhat differently from the term expectation of life. 
Thus at birth both expectation and duration of life according to 
the English experience of 1881-90 was 43-66 years for males; 
while at the age of 30 years the expectation of life for males was 
32-52 years, and the true mean duration of life for men aged 30 
years was 30 -f- 32-52 = 62*52 years. In other words at all ages 
after birth the mean duration of life is the present age added to 
the expectation of life. This distinctive use of the term " duration 
of life " is not adopted by Milne and Farr, and is only mentioned 
here to avoid possible confusion in reading the literature of life- 
tables. 

The Expectation of Life (synonyms : mean after-lifetime, mean 
duration of life, vie moyenne) is found as already described (p. 261) 
from a life-table. A life-table shows how many of a given 
number, started Avith at a given age, live through each subsequent 
year of life, and what is the sum of the number of years they 
live. The expectation of life is obtained by dividing the sum 
of these years by the number living at the year of age from 
which the expectation of life is desired. 



THE DURATION OF LIFE. 



299 



—< ^ 



a ^ 



2§ 
■Si 


m 

c 
l2 


00(N010(MO«D5DOu:J«OCOO«0«--.000'--'VO»0-^ 
.- 93 rH >ft ■* W ^ <p p in CN rH 05 t_-~ <p p «:- «.-- >p 

^-4^^,ll(i>(^^oo4^^.^^-■^o^~4t^l-^oo<»'OCO(^l(^^^-^ 

TltlOlrt'<}<-<J<C<5eOCO<M<N<Ni-lr-li-l 


"3 


«0 I^ ^ <N <M u"5 03 -^ C CO l_-- OD l^^ p 7^ >p 'T'" <^ '.~~ ?^ 
(?3C<)03-^oi)CJ00>0'M00mC^O00«0'*C0(N'-'rH 


3 cj 

ll 


a 

fa 


(^^GO'x>eo«^oorHO^£>?ococO'l^(^ll0^^pooo^-.CJ 

C0Oi^OC003'^C3':r<O^0^C^'^0iG0(MG0p»^p 
THir5-^-^-*COCO0Tl(MtM(Mt-l.-lr-H 


"3 


Ot~.OT-lO00O-*Ot^OVOTj(l0t^Tj<03«D«Dr^r-i 

coooo^-^to'i— !cocooc303'-iip<>Jooi;->p^pP 
.^oi--cTia3m(Moovr:>c-)coic5coocc«DTtic<5(N(Ni-H 


English Life-Table, 
No. 3, 1838-54. 


s 
fa 


loeot^ooi-*— i03-*«5ioeo^T-<ejeo«ooorH03jo 

00C0C003(MO00vOC<5pi>--JfC0>pppC0pp<Nr~ 

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030>t^<»a3i(N03'i>'>>03«3C0O00«Drt<e0(NC<lr--l 
SO-^-^-^COCOCOtNC^tNT-ti-trHi-l 


English 1 
Life- 1 
Tablft, 
No. -2. 




fa 


lC^O'r>^oo>p>;-|p^~opp«op^~ 1 . . 


English 
Life- 
Table, 
No. ]. 


^-lO(N50cooo■5^^>ploopI^pT-H^^^-rH^-.^>.r-l . 


1| 
0=^ 


t^(^^«)OOC3(^3pp^P'7^^|^oootNpvft.-l!^^o(^^ 




lnooii■coocou-5(^JOoo^n(^^oco^■q^eclC<^o 1 

MTt<COCO00C0<M(N'?JC^i-li-l'-l'-l 


De 

Moivre's 
Hypo- 
thesis. 


cooooioMOooiocooooiocoooomcoo 1 1 1 

■ T3(-#COCOCOCO(N<NI^(NrHi-li-H'-l 

1 













300 



VITAL STATISTICS. 



For the expectation of life in selected healthy districts of 
England see p. 308. 

A number of local life-tables have been constructed, based on the 
experience of the decennium 1881-90, and a comparative view of 
English experience in different localities can thus be obtained : — 

Expectation of Life. 



Years 
of 


MALES. 


London* 


Brighton t 


Portsmouth 


Mancliester { 


Oldham t 


Haydock, 

Lane. § 
(Hayward) 


Glasgow 


Age 


(Murphy) 


(Newsholine) 


(Mumby) 


(Tatham) 


(Tattersall) 


(Chambers) 










Town- 
















ship City 











40-66 


43-59 


43-68 


28-78 34-71 


36-88 


46-17 


35-18 


5 


50-77 


52-87 


52-86 


40-53 45-59 


46-90 


53-81 


46-97 


10 


47-22 


49-12 


48-64 


37 47 42 75 


43-81 


50-12 


44-32 


15 


42-88 


44-67 


44-27 


33-56 38-78 


39-59 


45-91 


40-51 


20 


38-70 


40-55 


4006 


29-61 34-62 


35-73 


41-45 


36-90 


25 


34-70 


36-51 


36-10 


26-00 30-69 


31-96 


37-00 


33-29 


35 


27-39 


29-02 


28-75 


20-01 23-76 


24-82 


28-81 


26-06 


45 


2100 


22-36 


22-06 


14-93 17-80 


18-44 


21-98 


19-54 


55 


15-31 


16-48 


15-98 


10-96 12-49 


12-83 


15-24 


13-39 


65 


10-59 


10-96 


1034 


7-48 8-15 


8-05 


9 


9-38 


75 



7-20 


6-64 


5-76 


4-74 5-11 


4-93 




5-96 


FEMALES. 


44-91 


49 25 


46-02 




40-75 


46-95 


37-70 


32-67 38-44 


5 


54-42 


57-36 


53-45 


43-66 48-06 


49-97 


54-41 


48-27 


10 


50-95 


53-60 


50-39 


40-94 45-43 


46-44 


50-37 


45 44 


15 


46-65 


49-26 


46-37 


37-05 41-50 


42 33 


46-20 


41-59 


20 


42-45 


44-95 


42-23 


33-08 37-33 


38-47 


42-11 


38-00 


25 


38-34 


40-68 


38-30 


29-41 33-38 


34-65 


38-36 


34-60 


35 


30-69 


32-69 


30-97 


22-90 26-30 


27-63 


30-98 


28-06 


45 


23-80 


25-30 


24-14 


17-20 19-79 


20-57 


2307 


21-61 


55 


17-34 


18-48 


17-46 


12-25 13-91 


14-10 


16-30 


15-60 


65 


11-78 


12-19 


11-08 


8-54 9-11 


8-87 


9-91 


10-69 


75 


7-79 


6-97 


6-12 


6-03 5-76 


5-16 


5-35 


6 97 



* The London Lifc-TaLle -was calculated by Farr's "short method." 

t The Brighton and the Oldham Life-Tables were constructed by the 
graphic method. 

+ Dr. Tatham has constrncted three life-tables for Manchester : for 
Manchester city, including all the townships of which it consists ; for 
Manchester township, the central and most crowded part of the city ; and 
for Manchester outlying townships. 

§ The Haydock Life-Table was calculated by a modified short method. 



THE DURATION OF LIFE. 301 

It should be observed that the expectation of life is the average 
number of years which persons of a given age, taken one Avith 
another, live, assuming that they die according to a given table of 
the probabilities of life. The term "expectation of life" does 
not imply that an individual may reasonably exi^ect to live a 
given number of years. The excess of those who die late is 
distributed among those who die early, "those who live longer 
enjoying as much more in proportion to their number, as those 
who fall short enjoy less of life." Thus the expectation of life 
has no relation whatever to the most probable lifetime of any 
given individual. 

jNIany attempts have been made in the absence of a life- table 
to ascertain the expectation, but none of them give trustworthy 
results. 

The formula of Willich gives approximate results for ages 
between 25 and 75. 

It is as follows : — 

If X - expectation of life, and a = present age, then 
X = f (80 - a). 

Thus at the age of 45 years the exjiectation of life according 
to this formula = §(80 — 45) = 23-3 years. According to the 
English Life-Table (p. 299) it varies from 22 for men to 24 for 
women. 

Dr. Bristowe's formula has been already given, and its limita- 
tions explained (p. 295). Dr. Farr gave the following formula, 
for obtaining an approximation to the expectation of life at birth 
when the birth-rate and death-rate are known. 

11 b - birth-rate and d = death-rate per unit of population, then 

the expectation of life = (*^x-)-f(-x---). 
\3 dj \3 hj 

Thus in the decennium 1881-90, the birth-rate in England and 
Wales was -03234, and the death-rate -01908 per unit. The 

expectation of life ^ (| x -^) + (I x ^^g^g-^) - 45-6 years, while 

the expectation of life shoAvn by the English Life-Table for males 
and females combined was 45*4 years. 

These formulae might be used without misleading to any con- 
siderable extent when applied to a given community for successive 
years. They would be misleading if employed for comparing com- 
munities having widely different birth-rates. 



302 VITAL STATISTICS. 

Probabilities of Life. It is sometimes desirable to ascertain 
not only the probable duration of life, but also the probability of 
dying Avithin a given period. 

In mathematical language, the words chance and prohahility are 
used as synonymous; but in common language the first word is 
used when the expectation that an event will happen is small, and 
the second when it is large. 

If the number of possible events = a + h, of Avhich a are 
favourable and h unfavourable, and if p = the probability of a 
favourable event happening, and q — the probability of an unfavour- 
able event happening, then, on the supposition that one of these 

events happens, jj = —^ ; q = — — • where p + q=l,ov certainty. 

Thus, if we wish to find the probability of a man aged 30 
living till he is 50, and also the probability that he will die before 
that age, we consult the life-table for males. From this we find 
that the number living (out of a million males born) at 30 is 
669,279 ; at 50 is 517, 639. Therefore the probability of a man 

aged 30 living to 50 = --. 

° ° 669279 

And as 669,279 - 517,639 = 151,640 = the number dying during 

fi ■ ^ ,^ f 151640 T 517639 , . .,., . 

the period; therefore -^^^^^, or 1 - ^^^^ = probability of 

dying between 30 and 50. 

If there be several independent events, the probabilities of 
the happening of which are resj^ectively p-^, j)^^ p^, etc., then 
the probability that all the events Avill happen is jp^ Xi^2 ^.Ps ^ ®^^-j 
that all will fail {l-p>i) (I-P2) (^-Ps) ^^^-'y ^^^^* ^^ ^^^^^ ^^^ 
event Avill happen, l-(l-jjj) {1-2X2) (l-p^) etc.; and that 
exactly one will happen and all the rest fail, j>^(l -p^) (1 -J^s) 
etc. +P2{1 -2^^) (1 -Ps) etc. +p^{l -^jj (1 -p^) etc. + etc. 

Thus, if ^ = r and p-^ = -, then the probability that both 

0/ + c? C + ft 

Avill happen is x — — . and the probability that neither will 

^^ a+h c+d ^ ^ 

happen is this amount subtracted from unity. 

Thus, the probability that a married couple — the husband's age 
being 40, and that of the wife 35 — will both live 15 years, is 
obtained as follows : — 



THE DURATION OF LIFE. 303 

By the English Life-table, 1881-90, out of 1,000,000 of each 
sex at birth, there are — 

Of males at 40 years old, 604,923 ; at 55 years old, 462,981. 

Of females „ 35 „ 638,912;,, 50 „ 516,375. 

The probabilitj'- of both these persons surviving 15 vears 
f ,-, . , 462981 516375 , . , i , " • 

from their present age = qq^^ x 630919' ""^'^^^^^^ product gives 

the required result. 



CHAPTER XXV. 



CHANGES IN THE ENGLISH EXPECTATION OF LIFE. 



IT is plain from the facts detailed in the next chapter, that in 
1871-80 the death-rate among adults was somewhat higher 
than it had previously been, while that at earlier ages was 
considerably lower, but that in 1881-90 there was no further 
increase in the adult death-rate, although persons over the age 
of 45 only shared to a slight extent in the marked decline in the 
death-rate at earlier ages, which had been showing itself. 

The following table brings the comparison up to recent years : — 

Annual Death-bates per 1000 Living at Twelve Age-periods 
IN Groups of Years. England and Wales. 







MALES. 


Period. 


All 
Ages. 


0- 


5- 


10- 


15- 


20- 


25- 


35- 


45- 


55- 


65- 


75- 


85 and 
upwards. 


1886-90 . 
1891-95 . 

1SS6-90 . 
1S91-95 . 


20-0 
19-8 

]7-S 

ir-7 


61-9 
62-1 


4-9 
4-5 


2-S 
2-5 


4-1 
4-0 


5-5 
5-3 


7-4 
7-2 


12-0 
12-2 


19-4 
19-8 


85-2 
86-3 


72-1 
71-9 


147-9 
149-9 


313-8 
290-6 


FEMALES. 


52-0 
52-0 


4'9 
4-5 


2-9 
2-7 


4-1 
4-0 


5-2 
4-9 


0-9 

6-7 


10-3 
10-3 


15-0 
15-3 


28-8 
29-S 


61-7 
62-8 


132-3 
136-1 


276-2 
263-8 



The death-rates shown in the above table may be described 
as practically stationary. It is highly probable that influenza and 
its complications are responsible for the fact that 1891-95 does 
not compare more favourably than it does with 1886-90. 

A cursory perusal . of the preceding facts may suggest the con- 
clusion that, as there has been but little decline in the death-rate 
affecting those who are living in the most useful working period 
of life, the gain to the community is correspondingly small. 

But such a view of the matter loses sight of the important 
fact that a larger projjortioii of those horn survive to the non- 
dependent or useful ages. This is brought out by the life-table ; 
and the only non-fallacious method of studying this question is 

304 



ENGLISH EXPECTATION OF LIFE. 305 

by means of a life-table founded on tbe number living and the 
number dying at each age. 

The facts are so well summarized by Dr. Tatliam in his account 
of the English Life-Table for 1881-90, that his account is repro- 
duced here verbatim. 

"Males. r»y the table of 1838-54, a million males born are 
reduced to half a million during the 45th year of age ; by the 
Uihle of 1871-80, this amount of reduction is not reached until 
the 48th year, and by the new table it is further postponed until 
the 52nd year. At the end of the first year of age the number 
of survivors by the new table occupies an intermediate position 
between the numbers by the two previous tables ; at every other 
age until 79 the new table shows a larger number of survivors 
than is shown by either of the older tables; from age 84 onwards, 
the survivors are fewer by the new table than by either of the 
others. This change is i')robably due, in part at least, to more 
accurate statement of age in recent than in earlier years. 

"The average lifetime of males, or the expectation of life at 
birth, which had lieen 39'91 years by the first of the three life- 
tables, and 41 "35 years by the second, is further increased by 
the new life-table to 43*66 years; that is to say, a male exposed 
throughout life to the rate of mortality obtaining in England and. 
Wales in 1881-90, would on an average live 2 '31 years longer 
than he would have lived had he been subject to the rates 
prevalent in 1871-80, and 3-75 years longer than he would 
have lived had he been subject to the rates prevalent in 
1838-54. In the last decennial report it was shown that 
the expectations of life among males by the life-table therein 
published were higher than those by the earlier table for ages 
below 19, equal thereto at age 19, and loAver at all subsequent 
ages. The new life-table shows improved expectations of life, ■ 
compared with those in the earlier tables, up to 26 years of age ; 
from age 27 until age 44 the expectations are lower thaii those in 
the first table, but higher than those in the 1871-80 table; for 
ages 45 and upwards the expectations of life are lower by the 
new table than by either of the others. 

"According to the first life-table, the 495,770 survivors at age 
45, out of a million males born, will live about 11,284,000 years 
of life, or an average of 2 2 "7 6 years each ; according to the 
second life-table the 522,374 survivors at the same age will live 
about 11,529,000 years of life, or an average of 22-07 years each; 
and according to the new life-table the 564,437 survivors at the 



306 VITAL STATISTICS 

same age will live 12,451,000 years of life, or an average of 22-06 
years each. The successive additions to the working time of life 
may be shown in a striking form by considering tlie years lived 
between the ages 20 and 60. A short calculation shows that 
the average numbers of years lived between these limits of age 
by each male born are 20*92, 22-00, and 23-56, respectively, 
according to the three life-tables. 

" Females. By the two earlier tables a million female children 
born were reduced to half a million in the 47th and 53rd years 
of age respectively; by the new table this amount of reduction 
is not reached until the 57th year. As in the case of males, 
the number of infants surviving at the end of the first year 
of life by the new table is intermediate between the numbers 
similarly surviving by the earlier tables. At all other ages until 
85 inclusive the numbers surviving are greater by the new table 
than by either of the others ; but as is also the case among males, 
the numbers of survivors at extreme ages diminish more rapidly 
by the new table than by either of the older ones. The ex- 
pectation of life at birth, which had been 41-85 years and 44-62 
years respectively in the earlier tables, is further increased by 
the new table to 47-18 years. The expectations at the several 
ages up to 44 years are greater by the new table than by either 
of the others. At age 44 and again at age 45 the expectations 
of life by the three tables are practically equal, being 24-72, 24-74, 
and 24-75 respectively at age 44, and 24-06, 24-06, and 24-05 
at age 45. At all ages beyond 45, the expectations of life are 
less by the new table than by either .of the previous tables. 
The average numbers of years lived between the ages 20 and 60 
by each female born are 21-65, 23-48, and 25-12 by the three 
life-tables respectively." 

It is clear from the above facts, even when 1871-80 is com- 
pared with 1838-54, that, as pointed out by Dr. Ogle, the 
survivors at the end of the 45th year are so much more numerous 
than they were under the rate of mortality prevailing in 1838-54, 
that "they can support the higher mortality of after years for 
a considerable period and yet retain their numerical superiority." 
Thus the aggregate life of the community at the most useful 
years of life is greater than under former conditions. This is 
true to a much greater extent for 1881-90, when the death-rate 
in adult life was lower than in the preceding decade, and the 
number of survivors from earlier ages was greater than in either 
of the tAvo preceding national life-tables. 



ENGLISH EXPECTATION OF LIFE. 



307 



The student's attention may be called in passing to a comparison 
of tlie tables on pp. 315 and 307 (below). The first table shows 
that the death-rate among males was lower, w4th a solitary and 
slight exception, at every age period in 1881-90 than in 1871-80. 
The second table shows the apparently inconsistent fact that, 
notwithstanding the lower death-rate, the male expectation of life 
was less favourable at ages over 45 in 1881-90 than in 1871-80. 
The key to the anomaly is found in the fact that the expectation 
of life at any given age takes into account the total number 
of survivors from all lower ages, and these were more numerous 
out of a given number at birth, according to the experience of 
1881-90, than according to that of 1871-80. 

For the purpose of easy comparison the facts tabulated on p. 299 
may be shown by differences as follows : — 

Increase or Decrease of Expectation of Life at Five-Yearly 
Intervals of Age, the English Life-Table for 1871-80 being 
compared with that for 1838-54, and the English Life-Table 
for 1881-90 with that for 1871-80. 





MALES, 


FEMALES, 


Age. 


Increase or Decrease of 


Increase or Decrease of 






1 




1871-80 


1881-90 


1871-80 1 lSSl-90 




comijared with 


coinpared with 


compared with compared with 




1S3S-54. 


1871-80. 


1838-54. 1871-80. 


. . . 


+ 1-44 


+ 2-31 


+ 2-77 


+ 2-56 


5 






-f 1-16 


-t-1-88 


+ 2-75 


-I-1-S4 


10 






-FO-55 


-H-40 


+ 2-09 


+ 1-34 


15 






-hO-23 


+ 1-06 


+ 1-73 


-fO-92 


20 






-0-08 


+ 0'87 


+ 1-37 


-f-0-76 


25 






-0-44 


+ 0-60 


+ 0-94 


-i-0-52 


30 






-0-66 


-fO-42 


+ 0-60 


-H0-S5 


35 






-0-76 


4-0-27 


-I-0-31 


+ 0'26 


40 






-0-76 


+ 0-12 


-)-012 


+ 0-14 


45 






-0-69 


-0-01 


0-00 


-0-01 


50 






-0-61 


-0-11 


-0-07 


- -0-12 


55 






-0-50 


-0-21 


-0-10 


-010 


60 






-0-39 


-0-26 


-010 


-0-14 


65 






-0-27 


-0-24 


-0-07 


-0-16 


70 






-0-18 


-0-23 


-0-07 


-0-18 


75 






-0-15 


-0-24 


-0-06 


-0-19 


80 






-0-14 


-0 27 


-0-06 


-0-20 


85 . 






-0-17 


-0-27 


-0-10 


-0-17 


90 . 






-0-18 


-0-29 


-o-ii 


-0-15 


95 . 






-0-16 


-0-29 


-0-12 


-0-12 



308 



VITAL STATISTICS. 



The real facts of the case are brought out clearly when the 
figaires contained in the fourth column of the life-table on p. 275, 
or the corresjDonding figures in other life-tables are examined. 
The number in this column opposite any age represents the total 
number living at all higher ages, or the total number of years 
lived by them. Thus in the Brighton Life-Table 51,195 males 
born live 2,206,174 complete years, 38,283 living at the fifth 
year of age subsequently live 2,005,945 complete years. 

Hence 2,206,174 - 2,005,945 = 200,229, the number of complete 
years lived between birth and 5 years of age, and the average for 
each is obtained by dividing by the number living at the earlier age. 

In the foUoAving table {Registrar-GeneraV s Decennial Supplement, 
part ii. jd. cxiv) Dr. Tatham shows how the mean lifetime or expec- 
tation of life is distributed in six life-tables over several life-periods. 



Life Period. 


Age-limits 
of Period. 


Length 

of 
Period 

in 


England and Wales. 


Man- 
chester 
Town- 

shij). 


Selected 
Healthy 
Districts. 
















Years. 


1838-54. 


1871-80. 


1881-90. 


1881-90. 


1849-53. 


1881-90. 


Infancy- 


0-5 


5 


MALES. 


3-94 


4-01 


4-02 


3-51 


4-29 


4-30 


School age . 


5-15 


10 


6-92 


7-11 


7-35 


5-95 


7-88 


8-13 


Adolescence . 


15-25 


10 


6-51 


6-79 


7-12 


5-55 


7-50 


7-89 


I 


25-35 


10 


5-95 


6-29 


6-69 


4-90 


6-95 


7-49 


Maturity . < 


35-45 


10 


5-31 


5-62 


6-04 


3-89 


6-37 


6-95 


45-55 


10 


4-54 


4-76 


5-16 


2-71 


5-72 


6-25 


( 


55-65 


10 


3-55 


3-63 


3-96 


1-51 


4-82 


5-22 




65 and up- 
















Decline 

Total . 


wards 


— 


3-1^ 


3-14 


3-32 


0-76 


5-03 


5-25 


All ages 


— 


39-91 


41-35 


43-66 


28-78 


48-56 


51-48 


Infancy 


5 


5 


FEMALES. 


4-07 


4-14 


4-17 


3-71 


4-39 


4-43 


School age . 


5-15 


10 


7-19 


7-40 


7-68 


6-32 


8-07 


8-41 


Adolescence . 


15-25 


10 


6-73 


7-07 


7-44 


5-92 


7-61 


8-12 


/ 


25-35 


10 


6-12 


6-58 


6-99 


5-35 


7-00 


7-69 


Maturity . I 


35-45 


10 


5-46 


5-95 


6-38 


4-50 


6-37 


7-15 


45-55 


10 


4-73 


5-20 


5-63 


3-42 


5-71 


6-53 


\ 


55-65 


10 


3-82 


4-21 


4-55 


2-16 


4-89 


5-60 




65 and up- 
















Decline 

Total . 


wards 


— 


3-73 


4-07 


4-34 


1-29 


5-41 


6-11 


All ages 


— 


41-85 


44-62 


47-18 


32-67 


49-45 


54-04 



ENGLISH EXPECTATION OF LIFE. 



309 



Comparing the three national life-tahles with each other, it will 
be seen that the expectation of life has improved at all age-periods, 
and not only at the earlier age-periods, in wliich the chief reduc- 
tion of death-rate has occurred. 

Dr. Tatham has summarized the teaching of the above table in 
the following : — 





England and Wales. 


Manchester 

Township, 

1881-90. 


Selected Healthy 
Districts. 


1838-54. 


1871-80. 


1881-90. 


1849-53. 


1881-90. 


Average lifetime "i Males . 
between 15 and - 
65 years of age . j Females 

Percentage of the Males . 
entire age-period > 
of 50 years, 15-65 ) Females 


25 86 
26-86 


27-09 
29 01 


28-97 
30 99 


18-56 
21-35 


31-36 
31-58 


3380 
35-09 


52 

54 


51 

58 


58 

62 


37 
43 


63 

63 


68 
70 



Taking the age 15 to 65 to represent the effective or working 
period of life, it will be seen that men on an average have a longer 
lifetime in this period of life, according to the experience of 
1881-90, than in either of the earlier life-tables. 

It is somewhat remarkable that in all the above six life-tables 
the proportion of the total lifetime which is lived between the 
ages 25 and 55 differs very little from 40 per cent. Dr. Tatham 
adds : " It follows that in each of these .six life-tables about 60 
per cent, of the average lifetime is lived partly before 25 years of 
age, and partly after 55 years of age ; and the distribution of this 
60 per cent. iDetween the earlier and the later ages Avould there- 
fore enable us to distinguish between life-tables for healthy and 
for unhealthy districts or periods without referring to the re- 
spective mean lifetimes." 

Healthy Districts Experience. The basis of experience on 
which the new Healthy Districts Life-Table has been calculated 
is stated on p. 289, and the facts as regards infantile mortality in 
this life-table are given on p. 123. The tables on pp. 308 and 309 
will enable a more complete comparison for other age-periods to be 
made between the two Healthy Districts Life-Tables and Life- 
Tables for Manchester Township, and for the whole of England 
and Wales at different periods. 



310 VITAL STATISTICS. 

Local Experience. A similar comparison between the experience 
of different great towns in the decennium 1881-90 can be made 
by means of the data which are summarized on p. 300. 

Life Capital. In a valuable Report on the Health of Greater 
MancJiester, 1891-93, Dr. Tatham has shown how the life-table 
may be applied to ascertain what he happily describes as the life- 
capital of a community. As already seen, the number of persons 
living at any age in a life-table represents a certain number of 
years of life, which number is measured by their expectations of 
life as shown in the life-table. 

The following formula gives the means for determining the 
mean expectation of life or after-lifetime of persons in groups of 
ages, like those in which death-rates are usually stated. 

The future lifetime of Ix persons is Qx, and the mean expectation of 
life of each of these persons is 9^. The future lifetime of Px persons 

p 
living at all ages between x and x + 1 is Q— -^, the mean expectation 

of life of each being ^ -l- The future lifetime of Px+Px+\+ 

Px 

+ Px+n-i persons living at all ages between x and x + nis 

{Qx + Qx+1 + + Qx+n-l}-l{Px+Px+l + +Px+n-l] 

and their mean expectation of life is 

Qx + Qx+l + Qx+n-l _i^ 

Px+Px+l +Px+n-l 

In the above formula it will be noted, to take an example, that not 
only does 

p = h±h i3^t that also 

5 2 ' 

Thus in the English Life-Table 
P =382 921 = ^?ii^^i^^Hl^. Also.P,^381410-f?^2^382,921. 

The method can be shown by the following illustration from 
the Brighton Life-Table. In addition to the columns printed on 
p. 275, "two further columns are required, viz., Px, the mean popu- 
lation for each year of life, and Qx the population or years of life 



ENGLISH EXPECTATION OF LIFE. 311 

lived in and above each year. For all years of life except the 
fir.st Px is taken as the arithmetical mean of l^ and Ix+ii as in the 
Englisli Life-Tal)le for 1881-90. For the first year of life a 
special method is required. 

(a) In the English Life-Table, 1881-90, it is assumed that each 
male dying during the first year of life enjoys •37539 year of Hfe, 
and each female "38280 year. 

This figure is obtained as follows. According to the English Life- 
Table for males 

Mean population Q-l = Po = 457817 
Population at age l = ?i =427184 

Difference = 30633 
This is the number of years lived by the do — 81996 males dying 
during the first year of life. 

,", the average lifetime of the males dying in the first year of 

life = ^^|g = . 37539 year. 
81996 ^ 

If we assume that the same proportionate amount of life holds 
good for those dying in Brigliton in the first year of their life, then 
h-h^ 51,195-43,315 = 7880 

= the number of males dying in 
the first year of life. 
7880 X -37539 = 2958 = number of years lived by those dying in 
the first year of life. 
But those surviving to the end of the first year live 43,315 years. 
.-. 43,315 + 2958 = 46,263 = total number of years lived in the 
first year of life, i.e., the mean population for that year. 
In subsequent years the arithmetical mean is taken, i.e., 

2 ""■ 

For the sake of convenience the above method has been 
adopted here. 

(b) It Avould have been practicable to deduce the mean number 
living 0-1 from the recorded proportion of deaths occurring at 
each month of the first year of life. Thus 51*1 per cent, of the 
deaths under one occurred under 3 months of age, 22*2 per cent, 
at ages 3-6 months, 14*5 per cent, at ages 6-9 months, and 12*2 
per cent, at ages 9-12 months. 

To obtain accurate results it "would be desirable to subdivide 
still further. Thus out of 114 male deaths aged 0-3 months, 
76 occurred under 1 month, and 44 under 1 week of age. 



312 



VITAL STATISTICS 



Applying the preceding formula to the Brighton Life-Table, the 
folio wino- result is obtained : — 





Sum of Mean 


Sum of Populations 


Mean Expectation 


Atje-groups. 


Populations for 


at each Age-group 


"of life in 




eacli Age-group. 


and upwards. 


groups of Ages. 


0- 4 . 


205692 


10876144-5 


52-88 


5- 9 . 






188760 


9748089-5 


51-64 


10-14 . 






185843 


9091081-5 


48-92 


15-19 . 






182875 


7887198-5 


43-13 


20-24 . 






178819 


6980593-5 


39-04 


25-35 . 






340826 


11336356-0 


33-26 


35-44 . 






280067 


8062297-0 


28-79 


45-54 . 






259762 


5187970-0 


19-97 


55-64 . 






219161 


2842473-0 


12-97 


65-74 . 






124983 


1183580-0 


9-47 


75-84 . 






50220 


282970-0 


5-60 


85 aud upwards 




6160 


22492-0 


3-65 



If we compare the actual number of deaths in Brighton in 
1897 with those which would have occurred had its population 
suffered from tlie mean death-rate of tlie ten years 1881-90, 
we obtain the following result : — 







Calculated 








Age-period. 


Mean 

Male 
Popula- 


Mean 
Deatli-rate 


number of 

Deaths in 

1S97 


Actual 
number 


Gain of 
Lives 


Gain of 

Life Capital 




tion in 
1S97. 


lSSl-90. 


according 
to the rates 


in 1897. 


in 1897. 


in 1897. 


• 






of 1881-90. 








0- . 


6218 


64-01 


398 


324 


4-74 


3913-12 


5- 






6340 


4-83 


31 


14 


-M7 


877-88 


10- 






5963 


2-30 


14 


10 


+ 4 


195-68 


15- 






5244 


4-13 


22 


20 


+ 2 


86-26 


20- 






4393 


5-05 


22 


19 


+ 3 


117-12 


25- 






8058 


7-72 


62 


45 


+ 17 


565-42 


35- 






6472 


12-94 


84 


70 


-t-14 


403-06 


45- 






4750 


21-17 


101 


88 


+ 13 


259-61 


55- 






3170 


32 76 


104 


87 


+ 17 


220-49 


65- 






1947 


64-36 


125 


114 


+ 11 


104-17 


75- 






727 


132-29 


96 


95 


+ 1 


5-60 


85 & upwards 


121 


293-8 


36 


22 


+ 14 


51-10 








53403 




1095 


908 


187 


6799-51 



ENGLISH EXPECTATION OF LIFE. 313 

The last column is obtained by multiplying each life gained by 
the superiority of 1897 over the mean of 1881-90 by the mean 
expectation of life for the corresponding age-period. Thus — 
52-88 X 74 = 3913-12. 

The gi'eater amount of saving at the earlier ages of life repre- 
sents a greater gain to the community than could have been fore- 
seen, apart from the application of the preceding method. 

The same method may be applied to the entire population of a 
community. Thus by multiplying the population at each age- 
group in the preceding table by the mean expectation of life for 
the same age-group, Ave obtain the total life-capital of the com- 

1 1 TP -PI Til 1"'l 1 

munity, and '-^-- — = average life-capital or future lifetime of 

population 

each member of the population. 

Furthermore, as mean population has been shown to be equal to 

o -.-r J J • population X 100 ,. 

years oi lite expended in a year, '- \ ^ — = proportion per 

life-capital 

cent, of life-capital expended in a year. 



CHAPTEK XXVI. 

THE DECLINE IN THE ENGLISH DEATH-EATE 
AND ITS CAUSES. 



WE have in chapter xv. p. 149 et seq. dwelt on the fall in the 
general death-rate, following on the passing of the Public 
Health Act of 1875. In order to determine the extent and value 
of this decline, it is necessary to study the deaths at varying 
ages in proportion to the number living at these ages, and the 
influence of the lower death-rate on the expectations of life at 
different ages. The necessary data for the first part of this study 
are contained in the following table : — 

Mean Annual Death-rate per 1000 in England and Wales 
AT Eleven Groups of Ages, in Groups of Years. 



PERSONS. 


Ages. 


1841-50. 


1S51-60. 


1861-70. 


1871-80. 


1881-90. 


All Ages 








22-28 


22-17 


22-42 


21-27 


19-08 


0- . 








66-03 


67-60 


68-30 


63-12 


56-82 


5-. 








9-03 


8-46 


7-95 


6-43 


5-29 


10-. 








5-27 


4-97 


4-47 


3-70 


3-02 


15- . 








7-46 


7-04 


6-39 


5-33 


4-35 


20-. 








9-28 


8-67 


8-19 


7-04 


5-61 


25-. 








10-25 


9-76 


9-79 


8-93 


7-53 


35-. 








12-85 


12-81 


12-72 


12-62 


11-42 


45-. 








17-03 


16-54 


17-30 


17-72 


17-06 


55-. 








29-86 


28-86 


30-28 


31-49 


31-33 


65-. 








63-59 


61-74 


62-45 


64-85 


64-65 


75 and upwards 




162-81 


159-78 


158-79 


161-59 


153-67 



The teaching of the preceding table is made plainer by stating 
the reductions in death-rate as percentages, as in the folloAving 



314 



DECLINE IN ENGLISH DEATH-RATE. 



115 



table in which 1881-90 is compared with 1871-80 for the two 
sexes separately : — 

Mean Annual Death-rate per 1000 in England and Wales at 
Eleven Groups op Ages, in Groups of Years, with Per- 
centage Differences. 



MALES. 


FEMALES. 








Increase or 






Increase or 








Decrease 






Decrease 








per cent, in 






per cent, in 


Ages. 


1871-SO. 


1881-90. 


1S81-90 com- 
pared with 
preceding 
Decennium. 


1871-80. 


1881-90. 


1881-90 com- 
pared with 
preceding 

Decennium. 


All Ages 






22-61 


20-22 


-10-6 


20-00 


18-01 


-10-0 


0- . 






68-14 


61-69 


- 9-5 


58-10 


51-99 


-10-5 


5- . 






6-67 


5-34 


-19-9 


6-20 


5-25 


- 15-3 


10- . 






3-69 


2-94 


-20-3 


3-70 


3-09 


-16-5 


15- . 






5-23 


4-30 


-17-8 


5-43 


4-40 


-19-0 


20- . 






7-32 


5-71 


-22-0 


6-78 


5-51 


-18-7 


25- . 






9-30 


7-73 


-16-9 


8-58 


7-34 


-14-5 


35- . 






13-74 


12-35 


-10-1 


11-58 


10-55 


- 8'9 


45- . 






20-05 


19-28 


- 3-8 


15-59 


15-04 


- 3-5 


55- . 






34-76 


34-66 


- 0-3 


28-54 


28-40 


- 0-5 


65- . 






69-57 


70-17 


+ 09 


60-82 


60-08 


- 1-2 


75 and upwards 


169-08 


162-18 


- 4-1 


155-83 


147-32 


- 5-5 



It will be seen that in both sexes the decline in the general 
death-rate, comparing the eighth with the ninth decade of this 
century, amounted to about 10 per cent. There was a decreased 
mortality among females at every age-period, and among males 
a decrease at all but the age-period 65-75. When comparing 
the eighth decade with the seventh Dr. Ogle had shown that, 
"speaking generally, the death-rates fell for the earlier age- 
periods, while they rose for the later periods of life" .... "the 
male death-rate being higher than in the preceding decennium 
at each period after 35 years of age, while the female death-rate 
did not show an increase until after 45 years of age." In 
commenting on the facts brought out in Dr. Ogle's decennial 
supplement for 1871-80, the writer several years ago made the 
following remarks, which may appropriately be quoted here 
(Brighton Life-Table, 1893, p. 25 ei .sw/.):— 



316 VITAL STATISTICS. 

" (a) A favourite explanation of the increased death-rate and 
diminished expectation of life in adult years is that, owing to 
the saving of life in the earlier years of life — a saving which 
has been especially in zymotic diseases and phthisis and other 
tubercular diseases — there has been a larger number of weakly 
survivors, who would under the former regime have been carried 
off by these diseases. In other words, the operation of the law 
of the survival of the fittest has been impeded, with results 
unfavourable to the health and vigour of adult life. This argu- 
ment assumes that weakly children are more prone to attack by 
infectious diseases than robust children, an assumption which 
experience does not confirm. These diseases appear to attack 
the majority of children, weakly or robust, who are exposed to 
their infection. It might be reasonably expected, therefore, that 
with a decrease in the total deaths from infectious diseases, there 
would have been at least a corresponding decrease in the number 
of those who are left maimed by an attack of one of these 
diseases to survive to adult life. We personally think that the 
weeding out of- weakly lives, caused by the greater mortality 
among weakly children suffering from an infectious disease, is 
almost entirely counterbalanced by the greater number of children 
made weakly in former times by non-fatal attacks of an infectious 
disease. 

" The case for deterioration of the race by survival of patients 
who would formerly have died in early life from phthisis and 
other tubercular diseases, appears to be a stronger one. It is 
probable that a larger proportion of phthisical patients are cured 
than formerly. It is probable also that many more children with 
a strong tendency to phthisis, or even suffering from its early 
symptoms, are prevented by the improved medical treatment and 
the improved social conditions of recent years, from developing 
the disease. These now may survive to adult life and become 
the parents of children with a strong tubercular tendency. 

" Such a fact need not, however, cause any serious apprehension 
for two reasons. In the first place, hereditary tendencies to 
phthisis only act under favourable predisposing conditions, such 
as damp and overcrowded houses, sedentary occupation in a 
cramped position, etc. ; and in presence of the active exciting 
agent, the specific hacillus tuberculosis introduced ab extra by 
inhalation or by means of food. 

"(6) Assuming that more phthisical patients survive than 
formerly, is it not equally true that fewer persons become 



DECLINE IN ENGLISH DEATH-RATE. 317 

plithisical than formerly 1 With a diminution of the active cases 
of phthisis, the nmnber of centres for phthisical sputum, which, 
as dust, is the chief cause of subsequent infection, must have 
diminished to a corresponding extent. Of the fact that the 
predisposing causes of phthisis — damp and overcrowded houses, 
ill-ventilated workshops, etc. — are steadily diminishing, there is 
evidence on every hand. It is, therefore, reasonable to suppose 
that much at least of the deteriorating effect of survival of tuber- 
cular persons is counterbalanced by the large number of persons 
who are ])r&ve7ited by ivq^roved scmitary and social conditions from 
becoming tubercular. 

" It is premature at present to attempt by statistical means to 
determine how far the counteracting influences Avhich are at work, 
balance each other, or failing a balance on which side is the pre- 
ponderating effect. 

" (r) The increased stress of modern life is supposed by many 
to explain the increased death-rate among adults. It is doubtful 
if such increased strain exists in the community as a whole. 
Each adult as he becomes year by year more deeply involved in 
the battle of life, comes to the conclusion that the general strain 
of life in the community is increasing, forgetting that the same 
causes operated as life advanced in previous generations. There 
is reason for thinking Avith Dr. Pye-Smith that much of the evil 
ascribed to ' over- pressure ' is really due to over-feeding and 
drinking. 

"Assuming, however, that over-pressure exists in certain 
stations of life, e.g., among city merchants, medical men, etc., 
it cannot be said to exist generally among professional men. 
Clergymen, lawyers, and civil-servants are as classes long-lived. 

" Even assuming that over-pressure exists throughout the whole 
of the professional and mercantile classes, these do not form the 
mass of the community. Hie majority of the po2ndation of 
England and Wales belong to the icage-earning classes, and the 
conditions of these classes will therefore necessarily have the 
greatest influence on the total result. What are the facts as 
regards these classes 1 They may be gathered from an important 
address by Mr., now Sir R Giffen.* He shows that the wages 
of the agricultural labourer have increased, while his hours have 
decreased. In the textile, engineering and house-building trades, 
he shows that the workman gets from 50 to 100 per cent, more 

* "The Progress of the Working Classes in the last Half-Centiiry." by 
R Giffen, f.k.s. (Inaugural Address, Statistical Society, Session 1883-84). 



318 VITAL STATISTICS. 

money than fifty years previously for 20 per cent, less work. He 
sums up in the following general statement : ' "While the Avork- 
man's Avages have advanced, most articles he consumes have rather 
diminished in price, the change in wheat being especially remark- 
able, and significant of a complete revolution in the condition of 
the masses. The increased price in the case of one or two articles 
— particularly meat and house-rent — is insufficient to neutralize the 
general advantages which the workman has gained.' 

" The conditions of housing of a large proportion of the wage- 
earning classes are still unsatisfactory, and leave ample scope for 
improvement, though they have immensely improved as compared 
with fifty years ago. It must also be admitted that there is a 
considerable (though probably a diminishing) residuum who are 
not included in the general improvement described by Mr. GifFen. 

"There are tAvo other circumstances affecting the life of the 
community Avhich must be considered in this connection. These 
are the effects of increasing ' urbanization ' and the associated 
increase of manufacturing (and largely indoor) occupations as 
contrasted Avith agricultural and outdoor occupations. 

"At the census of 1861, 37-7 per cent, of the total population 
of England and Wales AA^as rural; at the census of 1881 this 
l^roportion had decreased to 33 "4 per cent., and at the census of 
1891 to 28 '3 per cent. The urban death-rates are generally higher 
than the rural, though the former have shown a greater reduction 
in recent years than the latter. It is impossible to deny in toto 
that the conditions Avhich go to form the sum total of urban, life 
are less favourable to a healthy adult existence than those of rural 
life, though no attempt can be made at present to estimate the 
share of the increased number of the urban population in say 
1871-80 as compared Avith 1838-54, in producing the higher adult 
death-rate at the more recent period. 

" {d) Another consideration requires to be borne in mind. We 
are at present in a transition period. The Public Health Acts of 
1871 and 1875 heralded immense improvements in sanitation, the 
fruits of which have not even yet been fully reaped. There has 
been, more especially since 1875, steady and increasing improve- 
ment in the conditions under which people live. Men noAV-40 
years of age Avere born in the pre-sanitary period ; and the first 
20 years of their life Avere spent under more unhygienic conditions 
than those noAv holding good. This fact Avould go far toAvards 
explaining a stationary death-rate at the higher ages. It does not, 
hoAvever, explain an increased death-rate at those ages. 



DECLINE IN ENGLISH DEATH-RATE. 319 

"The explanation of this increased death-rate at the higher ages 
will i^robably be evident when at the end of another twenty or 
thirty years the improved conditions of life have endured suffi- 
ciently long to enable their full force and value to be determined. 
We must 1)0 content in the meantime to have stated the more 
important factors which appear to be at work, leaving the complete 
solution of the problem to a time when the statistical experience 
of our country is more mature." 

The preceding remarks have received, since they were Avritten, 
valualJe confirmation from the statistics of another decennium. 
The decline in the death-rate which when the eighth was compared 
with the seventh decade stopped short at adult life, has now 
extended to nearly every period of life in both sexes, though it is 
but small in amount after the forty-fifth year of life. 

Distribution of Decreased Mortality according to Cause. 

In the following tal)le the necessary data for a somewhat detailed 
comparison of the causes of death in successive periods are given. 
The caution given on p. 191 as to comparing death-rates from 
infectious diseases for groups of years must be held in remem- 
brance in making this comparison. The aggregate zymotic diseases 
show a considerable decrease, fever showing a remarkable decline. 
Among the other named diseases the most remarkable features are 
the great decrease in phthisis, and the increase under the heads of 
cancer, and of respiratory, circulatory, and urinary diseases. The 
question as to how far these recorded increases are real is discussed 
on pp. 238 and 242. 



320 



VITAL STATISTICS. 



Annual Mortality prom Several Causes per Million Persons 
Living at all Ages in Successive Periods and Years. 





1861-70. 


1871-80. 


lSSl-90. 


1891-95. 


All Causes ...... 


22416 


21272 


19080 


18738 


Small-pox . . . . . . 


160 


234 


45 


20 


Measles 


440 


378 


440 


408 


Scarlet Fever 


972 


716 


334 


182 


Diphtheria 


185 


121 


163 


253 


Whooping-cough .... 


527 


512 


450 


398 


Fever- | Typhus . . . ) 

^. ^1 ■,. I Enteric . . . } 

including) jjj_^^j5j^^^ . . ( 


885 


322 


14 
196 


174 




(l03 


25 


8J 


Puerperal Fever and ) 
Diseases of Childbirth . . \ 


165 


167 


153 


168 


Diarrhceal Diseases . . . . 


1076 


935 


674 


651 


Cancer 


384 


• 468 


589 


712 


Phthisis 


2475 


2116 


1724 


1464 


Hydrocephalus ..... 


347 


317 


( 696 


660 


Other Tubercular Diseases . 


437 


445 






Diseases of Nervous System (including ) 


2796 


2789 


2592 


2288 


Convulsions) . . . . j 










Diseases of Circulatory System . 


1054 


1339 


1576 


1677 


Diseases of Respiratory System . 


3591 


3899 


3729 


3747 


Diseases of Digestive System 


1184 


1165 


1104 


1116 


Diseases of Urinary System 


266 


350 


435 


453 


Violence 


765 


733 


648 


663 



CHAPTER XXVII. 

STATISTICAL FALLACIES. 

THE reservation of an entire chapter to the consideration of 
the fallacies into which those who employ figures frequently 
fall, appears almost as absurd as it would be to devote a chapter 
at the end of a treatise on grammar to the consideration of 
grammatical errors. The study of the science of grammar 
involves the exposure of grammatical errors ; and similarly, if 
we have been successful in our attempt to treat of the principles 
of vital statistics, the fallacies Avhicli we so frequently meet 
with in medical statistics may be considered to be already 
sufficiently exposed. But while this is logically correct, there 
is a practical convenience in presenting a concise summary of 
the more important statistical errors, and especially so as this 
Avill enable us to consider in detail several cases which have 
not arisen in the preceding chapters. 

"VVe may first of all cite Quetelet's four chief rules, which 
are worthy to be held in remembrance. 

(1) K'ever have preconceived ideas as to what the figures 
are to prove. 

(2) Never reject a number that seems contrary to what you 
might expect, merely because it departs a good deal from the 
apparent average. 

(3) Be careful to weigh and record all the possible causes of 
an event, and do not attribute to one what is really the result 
of the combination of several. 

(4) Never compare data which have nothing in common. 
Were these rules constantly followed, the science of statistics 

would be much more respected than it is, and the value of its 
results Avould be greatly increased. 

Errors already Exposed. In the preceding chapters, numerous 
instances have arisen, illustrating various phases of statistical 

Y 321 



322 VITAL STATISTICS. 

fallacies. Before considering other cases, it may be well to 
recapitulate those already mentioned. 

Population forms an essential datum in the presentation of 
all vital statistics, and inaccurate estimates of population vitiate 
every subsequent calculation. Instances of such inaccurate 
estimates are given at p. 8. The errors arising in connection 
with the statement of age, infirmities, etc., are given at pp. 2 
and 4. The age and sex constitution of the j)opulation has 
a great influence on the marriage-rate (p. 57), on the birth- 
rate (p. 71), and on the death-rate (p. 102); and unless due 
allowance be made for variation in composition of the population 
as to age and sex, especially as to age, serious errors will arise. 

A correct and complete registration of causes of death is 
another essential datum in the presentation of vital statistics, 
and the chief errors in this connection have been already 
discussed (p. 29). 

The questions of increase of cancer (p. 242), and of decrease 
of phthisis (p. 239) involve serious statistical difficulties, Avhich 
have been already considered. The fallaciousness of the as- 
sumption that a fixed ratio exists between sickness and mortality 
has been discussed (pp. 37, 185). 

We ha"ve stated that the birth-rate, to be strictly accurate, 
should be calculated in terms of the number of women living 
at child-bearing years (p. 72), and that the number of illegitimate 
births should not be stated in proportion to the total births (p. 82). 

The fallacies connected Avith death-rates for short periods have 
been pointed out (p. 86), as also the effect of migration of popula- 
tion in disturbing the death-rate (p. 87), the effect of public 
institutions on the same (p. 89), and the fallacies as to the 
correct relationship of birth-rate to death-rate (p. 96). False 
methods of estimating the mortality at different ages have been 
exposed (p. 116). The sources of error in connection with 
occupational statistics are discussed at page 174, and, among 
other additional fallacies which have been considered, we may 
mention those in regard to small-pox (p. 208 et seq.), and in 
regard to the duration of life as evidenced by the mean age at 
leath (p. 292). 

Classification of Fallacies. Without attempting a complete 
logical classification of fallacies, we may divide them into fallacies 
of observation and fallacies of inference. The errors which we 
shall consider will be found to come under one of these heads, in 



STATISTICAL FALLACIES. 323 

some cases illustrating them both, the data and the inferences 
from them being each inaccurate or incomplete, or both. 

Errors from Paucity of Data. The number of observations on 
which any deduction is founded should be considerable. The 
deduction is trustworthy in proportion as the observations are 
numerous, on the assumption that the latter are at the same time 
accurate and comparable. There is, unfortunately, nothing more 
common in medical literature than a crude generalization from 
insufficient data, especially as to the treatment of disease, ignoring 
the mathematical rule that the relative values of two or more 
series are as the square roots of the numbers of observations ; so 
that by increasing the number of observations in any inquiry, the 
accuracy increases as the square root of the number. The results 
obtained, even from a large number of observations, are, however, 
only an approximation to the truth, although the limits of error 
are reduced with each increase in the number of observations. 

The degree of apjjroximation to the truth of a varying number 
of observations can be estimated by means of Poisson's formula. 
This formula can, however, only be entirely trusted in the ideal 
case of games of chance, in other cases forming an inadequate 
test of accuracy. 

Let ju, = total number of cases recorded, 
m — number in one group, 
n — number in the other group, 
so that m + n = \i. 

The proportion of each group to the whole will be Respectively 
— and -. These proportions will vary within certain limits in 

succeeding instances, and the extent of variation will be within 
the proportion represented by 




and'^ o i^lm-n 



n _ 72? 

i V / 

It is evident that the larger the value of /x (t he tot al number of 
observations) the less will be the value of 2 / "'"^'^^ and the less 

will be the limits of error in the simple proportion — . 



324 



VITAL STATISTICS. 



Thus if out of ten cases of cholera seven recover, how near is 
this to the true average of recoveries 1 Here the probability of 
recovering is represented by -^q, of dying by -^q. The possible 
error is given by the second half of Poisson's formula. Thus, 



9 /2!!il*-o, / 2x^x3 . /J2__ 

"V M^ --"^v 103 --y 1000" 



4098. 



Thus the possible error is as •4098 to unity, or, in other words, 
the error is greater than the number of deaths. What will be 
the possible variation in 100,000 cases on this basis? 

The average, as stated, is 70,000 recoveries out of 100,000 
cases; the possible error is 40,980; therefore the number of 
recoveries may be either 29,020 or 110,980, a conclusion which is 
an obvious absurdity. 

If, however, 100 cases be collected, out of which seventy re- 
cover, the proportion is the same ; but by Poisson's formula the 
error is only -13 to unity, and the range of recoveries out of 
100,000 cases will lie between 

70,000 + 13,000 = 83,000, 
and 70,000 - 13,000 = 57,000. 

If 1000 cases are taken, of which 700 recover, the error will 
be only -04 to unity, and the range of recoveries in 100,000 cases 
will lie between ^q^qqq ^ ^qqq ^ 74^qOo^ 

and 70,000 - 4000 = 66,000. 

The following table will show more clearly how, with an in- 
creasing number of facts, the limits of possible error (assuming 
the accuracy of the facts recorded) steadily decrease : — 







Possible Number Recovering out of 


Total Number of 


Number of Recoveries. 


100,000 Cases according to Poisson's 


Cases. 




Formula. 


10 


7 


29,020 or 110,980 


100 


70 


57,000 „ 73,000 


1000 


700 


66,000 „ 74,000 


10,000 


7000 


68,700 ,, 71,300 


100,000 


70,000 


69,600 „ 70,400 


1,000,000 


700,000 


69,870 „ 70,130 



It is evident that a small number of observations is inadequate 
to establish a conclusion : but inasmuch as the degree of accuracy 
increases only in the ratio of the square root of the number of 



STATISTICAL FALLACIES. 325 

observations, the mere repetition of observations beyond a certain 
number (10,000 in the previous table) is proportionately of small 
value, and after a time becomes practically useless. 

Errors from Inaccuracy or Incomparability of Data. In- 
accuracy or incompleteness of data necessarily leads to fallacious 
conclusions. Apart altogether from any intentional deception, 
the trustworthiness and ability of the observer or recorder of 
a given set of facts is an important element in estimating the 
relial)ility of deductions from them. It is necessary that the 
data should be collected on a uniform plan, and should be of a 
strictly comparable nature. Any neglect in stating a single cause 
of variation in some of the facts may vitiate the entire conclusion. 
Thus it is well knoAvn tliat cholera is much less fatal towards the 
end of an epidemic than at its commencement. If, therefore, in 
stating the percentage of recoveries under a given method of 
treatment, no mention was made of the period of the epidemic 
when the cases came under treatment, a trustworthy conclusion 
would be impossible. The neglect of the precaution that the 
phenomena or events dealt with shall he strictly comparahle has 
given rise to the most valid objections which have been urged 
against the use of the numerical method in medicine. 

Dr. T. Graham Balfour, p.r.s., in his inaugural address as 
President of the Statistical Society (November, 1888), has given 
an interesting instance, arising from the alleged deterioration 
of recruits, of the fallacy due to overlooking the condition of 
"other things being equal," which we shall now summarize. 

It is stated, on the authority of the Director-General of the 
Medical Army Department, that in the years 1860-64 inclusive, 
no fewer than 32,324 examinations of recruits were made by 
army-surgeons ; and that the rejections from all causes were 
371-67 per 1000. During 1882-86, 132,563 men offered them- 
selves for enlistment, of whom 415-58 per 1000 were rejected, 
showing a marked increase in the jiroportion of rejections. Sir 
Thomas Crawford can explain this increase in the rejections in 
one way only : " the masses, from whom the army recruits are 
chiefly taken, are of an inferior physique to what they were 
twenty- five years ago." Dr. Balfour, hoAvever, instituted indejjen- 
dent inquiries, Avhich threw grave doubt on this conclusion, and 
satisfied him that a large proportion, at least, of the striking 
excess of rejections at the later period Avas due, not to an increase 
in the disabilities among the recruits examined, but partly to 



326 VITAL STATISTICS 

improvements introduced into tlie returns in 1864, by which they 
were made much more complete, and partly to changes instituted 
in 1879 and 1880 in the system of examination. 

Dr. Balfour's address must be consulted for full details, which 
make it clear that owing to the varying regulations in force in the 
army, it is impossible to arrange the results of the two series of 
years in a form Avhich complies with the condition of "other 
things being equal." 

Similar remarks apply to the question of height of recruits, 
and the proportion of recruits rejected in successive periods. 

Errors in Comparing Total Deaths in Successive Years. It is 

inaccurate to compare the number of total deaths or the number 
of deaths from any one disease with the corresponding number in 
any previous year unless some allowance is made for increase 
of population. Coeteris paribus, a larger population would supply 
a greater number of deaths than a smaller one. We shall now 
demonstrate the method by which tJie numher of deaths in any 
year may he compared witli the decennial average of the ten 
preceding years, corrected for increase of p)op)ulation during the 
period, taking as an example the number of deaths from measles 
in England and Wales in 1887, and the average number in the 
decennium 1877-86. 

The number of deaths from measles in 1887 = 16,765. 

The average annual number of deaths from measles in the ten 
years 1877-86-10,549. 

What Avas this average corrected for increase of population, in 
order to allow accurate comparison with the figures for 1887? 

Now, the population of England and Wales in 1887 = 
28,247,151. 

The mean popidation of 1877-86, obtained by summation of 
the populations in each year and division by ten = 26,256,699. 
The deaths from measles in the decennium 1877-86 must there- 
fore be raised in the proportion of 26,256,699 to 28,247,151, in 
order to bring them into true comparison with those of 1887. 

But ^^[151 = 1.075. 
26256699 

By multiplying 10,549 by 1-075 we obtain 11,340, which 
represents the average annual number of deaths from measles 
during the decennium 1877-86, corrected for increase of 
population. 



STATISTICAL FALLACIES. 



327 



This number, subtracted from 16,765, gives 5425, which is the 
excess of deaths from measles in 1887 as compared with the mean 
of the previous decennium. 

Errors in Regard to Averages. The larger the basis of facts 
on which an average is founded the more reliable it is. Acci- 
dental causes may produce large variations in a small series 
of observations, which become corrected when the facts are 
multiplied. It is on this principle that, in spite of the great 
annual fluctuations in the receipts and expenditure of Insurance 
Societies, tlie results l^ecome equalized for a series of years. 

Dr. Guy gives the following instance of the value of increas- 
ing the number of facts on which an average is based, from an 
investigation into the average age at death of members of the 
peerage and baronetage : — 



Number of 
Facts. 


Average Age at Death. 


Maximum. 


Minimum. 


Range. 


25 
50 
100 
200 
400 
800 

1600 


69-40 
66-44 
63-70 
62-38 
61-10 
60 84 


50-64 
55-20 
56-85 
57-61 
58-24 
59-97 


18-76 

11-24 

6-85 

4-77 
2-86 
1-17 


60-25 



If we assume the true average duration of life of the members 
of the peerage and baronetage who have attained 21 years to 
extend to 60 years, then, omitting decimal points, the following 
table shows the errors in excess or defect : — 



Number of Facts. 


Errors in Excess 
or Defect. 


25 
50 
100 
200 
400 
800 


9h 
H 
H 
24 

H 

Oh 



328 VITAL STATISTICS. 

It may haj)pen, however, that the first 25 observations in a 
table Hke the preceding would give as correct an average as 800 
observations; and there is always a balance of probability in 
favour of the average of even a small number of facts approxi- 
mating more closely to the true average than to the extremes. 
The extreme values, that is, the two ends of the scale, of which 
the average is the middle, should also be noted. As Dr. Guy 
puts it, "Averages are numerical expressions of probabilities; 
extreme values are expressions of possibilities." The possible 
range of the average obtained from a stated number of observa- 
tions can always be ascertained by means of Poisson's formula, 
thus indicating the possible amount of error. 

Although, as already stated, the average of a small number 
of facts may give a near approximation to the truth, such an 
average must be regarded as requiring a confirmation which the 
average from a large number of facts does not require. It is 
important to note also that the results obtained from an average 
can never he apjyUed to a particular case. An average is the 
mean result from a number of instances, all of which may be 
either above or below it, so that it does not necessarily express 
the exact truth in regard to any one of the cases on which the 
average is founded. 

The fallacies connected Avith the application of the results of a 
large number of cases to an individual instance are well known to 
insurance offices. General results from a large aggregation of facts 
may be safely applied to a similar aggregation of facts ; but their 
application to single cases is full of dangers. Thus, the mean 
duration of life, according to a life-table, expresses with almost 
mathematical certainty the average age at death of the members 
of a community taken one loitli another, but is not necessarily 
accurate when applied to a single individual. All that we can 
safely conclude is, that the excess of those who live longer will 
be counterbalanced by the deficiency of years of those Avho die at 
an earlier age than the average. 

Extremes, being the expression of possibilities, require a larger 
number of individual facts than averages to render them trust- 
worthy. Dr. Guy gives an interesting instance of neglect of this 
rule. M. Orfila stated that it Avas possible approximately to 
determine the stature of the skeleton and of the body by 
measuring one of the long bones. He did not test this, however, 
by taking extreme cases, but only by a rough average. It Avas 
subsequently found that out of seven ulnas, measuring in length 



STATISTICAL FALLACIES. 329 

10 inches and 8 lines, one corresponded to a stature of G ft. 1^ in., 
another to 5 ft. 5 in., implying a possible error of 8^ inches. 

In connection with public health, two fallacious uses of aver- 
ages must be discussed, viz., the fallacy of average strength, and 
of bed-mortality in hospitals, which are closely connected. 

Errors in Connection with Average Strength. The sickness 
and mortality statistics in the army and navy are calculated on 
what is known as the average sfrenrjth or 7nea7i force. It is not 
quite clear, from the annual report of the Army Medical Depart- 
ment, Avhether the mean force includes those on sick leave as Avell 
as detached men, but apparently these are included. In the navy 
the mean force has been recently made to include men on short 
terms of leave of absence and the sick under treatment in hospital 
— a change which has been found to increase the force by 3 per 
cent. According to Dr. Parkes, the average strength includes in 
the army the number of men of each regiment present at each 
station on the muster days, divided by the number of muster 
days. It thus includes the sick men in hospital as well as the 
healthy men, and is consequently not a completely accurate basis 
on which to determine the amount of disease among the healthy 
men. When many changes of troops occur, it is often difhcult to 
ascertain the mean strength, and erroneous calculations are con- 
sequently not uncommon. An example, quoted by Dr. Parkes 
from a paper by Dr. Balfour, may be cited, Avhich is of special 
interest, inasmuch as it affords an instance in which an unhealthy 
station in India (Masulipatam) was credited with a more favourable 
rate of mortality than it was entitled to. The Madras Medical 
Board stated that the death-rate among all the European regiments 
in the Presidency, from January, 1813, to December, 1819, was 
56 "9 per 1000; while that of the regiments at Masulipatam from 
1813 to 1832 inclusive was 51 '0 per 1000; and they inferred that 
the rate of mortality having been somewhat lower than throughout 
the rest of the Presidency for such a period, there Avas reason for 
concluding that the station could not be considered under ordinary 
circumstances as unhealthy. In arriving at the preceding death- 
rate for Masulipatam, however, the fact had been lost sight of, 
that in several of the years between 1813 and 1832, the regiments 
were quartered at Masulipatam during part of the year only. 
Under such circumstances, in calculating the annual death-rate, 
only such a proportion of the mean annual strength should be 
taken as corresponded with the period during which the regiment 



330 VITAL STATISTICS. 

was stationed there. If it Avas stationed there six months, the 
calculation should be based on half the strength ; if nine months, 
on three-fourths of it, and so on. 

When the necessary correction was made in the instance cited, 
the annual death-rate from 1813 to 1832 was found to average 
63'94 per 1000, instead of 51-00 as previously stated. 

Th'e error we have just described is similar to the assumption 
that, in a town Avith a population of 100,000 persons, and in 
which 3000 deaths occurred during nine months, the annual 
death-rate is 30 per 1000. The population should, of course, 
be reduced by one-fourth; and the annual death-rate, on the 
assumption that the same rate of mortality continues during the 
remaining three months of the year, is 40 per 1000. 

Fallacies of Hospital Statistics. Much of the misapprehension 
which has arisen in medical literature concerning hospital mortality 
is OAving to a lack of comprehension of the facts relative to 
average strength, Avliich AA''e have already adduced. The subject 
is discussed very lucidly in the Sixth Report of Mr. (noAV Sir 
John) Simon to the Privy Council for 1863; and Ave cannot give 
a better vieAV of it than by summarizing his argument, founded on 
an investigation made by Dr. BristoAve and Mr. Holmes into the 
sanitary conditions of, and results obtained in, various large 
hospitals. 

To begin Avith, the word "healthy," as applied to a hospital, 
evidently cannot denote that its inmates shall be persons in 
health ; nor that its inmates shall not have a high death-rate, for 
this is involved in the condition of the inmates. A "healthy" 
hospital is one " Avhich does not by any fault of its own (Avhether 
inherent fault, as of site or construction ; or fault of heeping, 
as dirtiness or overcroAvding) aggravate ever so little the sickness, 
nor oppose ever so little the recovery of persons Avho are properly 
its inmates." 

Death is unquestionably the most serious form in AAdiich lack of 
success in treatment is evidenced. It is essential, however, if 
hospital death-rates are to possess the slightest value, that they 
should be calculated on given magnitudes of illness. The com- 
parison of the death-rate in a fever hospital Avith that in an 
orthopoedic hosj)ital Avould obviously be absurd. Unless due 
regard be had, therefore, to the uncertain import of the word 
"patient," death-rates are Avorthless as evidence of success or 
failure in hospital treatment. It is notorious that hospitals, Avith 



STATISTICAL FALLACIES. 331 

regxarcl to the quality and magnitude of the cases received in them 
for treatment, differ enormously from one another. Large urban 
hospitals receive patients at any time and of the gravest character, 
and "wage an ever- precarious contest against the least conquerable 
forms of disease " ; while in many country hospitals admission is 
by subscriber's letter, there is a comparatively infrequent change 
of patients, and a minimum of severe or urgent cases. On the 
whole, it may be safely asserted that the hospitals with high 
death-rates have no reason to be ashamed, nor the hospitals with 
low death-rates to congratulate themselves. 

The Registrar-General published in his Twenty-fourth Annual 
Report some statistics of the different hospitals. The census on 
April 8th, 1861, showed how many special inmates were contained 
in each of the hospitals of England, while the death-returns of 
the year 1861 showed how many deaths occurred during the year 
in the same hospitals. From these materials an annual death-rate 
per 100 occupied beds, which may be called a hed death-rate, was 
compiled. Such bed death-rates are most misleading, (a) In the 
first place, they were calculated on the hospital population of a 
single day — that of the census, which may have been much above 
or below the average — and not on the average daily sick population. 
Dr. Buchanan showed that, accepting the number of inmates at 
the census day in 1861 as the basis of calculation, the bed death- 
rate of the London Fever Hospital in 1860 was nearly 30 per 
cent., in 1861 nearly 500 per cent., in 1862 nearly 2000 per cent., 
and in 1863 nearly 1400 per cent. 

{h) Each bed in a hospital usually receives during the year 
a succession of patients. All that a bed death-rate means is 
that there occurs in every occupied bed in a hospital a certain 
number of deaths per annum. A bed death-rate of 100 per cent, 
per annum means that on an average one death occurs during the 
year in every occupied bed of the hospital. 

(c) These objections, however, are trifling when compared with 
the objections already stated against all general death-rates as 
measures of hospital healthiness. A table given in the Registrar- 
General's report alluded to, shows the striking and suspicious 
disparity between the bed death-rates of different hospitals. 

Thus the Nottingham hospital had a bed death-rate under 41, 
while that of Manchester was over 130; at Swansea the death- 
rate was only 10, while at Bath it was 102, per 100 occupied beds. 

These results are quite untrustworthy. Assuming that the 
mortality in urban hospitals is twice as great as in rural hospitals. 



332 VITAL STATISTICS. 

then we might conclude any one of three things: "either (1) 
that the urban hospitals change their sick population twice as 
often as the rural hospitals, and that other conditions are equal; 
or (2) that in the urban hospitals the mean gravity of cases 
received for treatment is twice as great as in the rural hospitals, 
and that other conditions are equal; or (3) that in the urban 
hospitals the success of treatment of given magnitudes of disease 
is half as great as in the rural hospitals, and that other conditions 
are equal." In all probability the two first of these suppositions 
express the truth, though unfortunately Dr. Farr gave the 
authority of his name to the statement that general hospitals, 
by reason of "defects" which "render them ways of death to 
their inmates," do "not benefit mankind directly," but merely 
"as pathological observatories and medical schools"; and Miss 
Florence ISTightingale, in her Notes on Hospitals, has accepted Dr. 
Farr's conclusions as valid. The real fact is that general death- 
rates are inapplicable as tests of true differences of hospital success, 
and ought never to have been employed for this purpose. 

If general death-rates are employed at all in regard to hospitals, 
the true principle on which to calculate them is on the basis of 
the aggregate annual number of cases treated to a termination. 
This may be called the patient death-rate, as distinguished from 
the bed death-rate already described. There is no necessary 
connection between the range shown by bed death-rates in the 
preceding table and the range of patient death-rates in the same 
institutions. Whether the two ranges would correspond depends 
on whether the average time of staying in hos^ntal is the same in 
the hospitals compared. But as a matter of fact the staying-time 
varies enormously in different hospitals, being usually shorter in 
larger hospitals, and shorter in hospitals where the proportion of 
acute cases is high. If the mean stay of patients in hospitals 
is known, hed death-rates may at once be converted into patient 
death-rates or vice versa. 

It follows from the preceding considerations that comparisons 
of hospital statistics, if they are to serve any useful purpose, 
must be in considerable detail. Not only should cases of like 
nature be compared, but, inasmuch as the mortality from many 
diseases varies with age, the age-constitution of the patients of 
the institutions under comparison should be noted. A typhus 
patient aged 55 is at least ten times as likely to die as a typhus 
patient aged 15. Similarly the success of the operation of 
lithotomy varies greatly at different ages. 



STATISTICAL FALLACIES. 333 

The success of the major amputations again varies greatly 
according to the age of patients, and according to whether operation 
is required as the result of injury or disease ; and in regard to all 
statistics dealing with the results of treatment, it is desirable that 
the age and special circumstances of the individual cases should 
be fully stated. 

Errors from the Composition of Ratios. As a general rule, 
it is dangerous in dealing with deaths and other rates to combine 
or compound such rates. This error is so commonly fallen into 
that the following illustrations of the resulting mistakes cannot 
be considered superfluous : — 

Thus the population of — 

Battersea Avas 125,091 and its death-rate 20"00 
Putney „ 14,450 „ „ „ 13-70 

3^70 



Mean death-rate of the two = 16'85 

This, however, is a most incorrect result. The true method is 
as follows : — 

Battersea population, 125,091 ; deaths, 2503 
Putney „ 14,450 ; „ 199 

139,541 2702 

Therefore ~ — = 19*59 is the true death-rate. 

139,541 

The true death-rate is thus seen to be much higher than that 
first obtained, owing to the fact that in the first calculation 
equal prominence is given to the healthiness of Putney and of 
Battersea, although Putney had only one-eighth of the entire 
population. 

Another instructive and somewhat amusing instance is furnished 
by a correspondence in the Times during September, 1888. X 
wrote to the Times newspaper, and on the assumption that the 
death-rate in the British army at home and abroad in 1885 was 
11-12 per 1000, and the death-rate of troops at home 6-68, argued 
gravely that the death-rate of troops abroad was therefore 4-44 
per 1000 ! Y wrote to correct this statement, and pointed out 
that if X's, method were correct, then it would be equally true 
that if the death-rate of the English and Irish in the United 
Kingdom was 21 per 1000 and that of the Irish 20 per 1000, the 



334 VITAL STATISTICS. 

mortality of the English was only 1 per 1000 ; or if the death- 
rate of the Irish was over 21, then the English live for ever! 
Y then proceeded to maintain that the true mortality of the 
troops abroad was 15 "56 per 1000, without mentioning, as Z 
pointed out in a subsequent letter, that this was only correct 
Avhen the troops at home and abroad were equal in number ; on 
which Y replied that "rates per 1000 are quite irrespective of 
numbers at home and abroad" — a conclusion which is true for 
rates regarded separately, but flagrantly false when applied to 
their conrposition. As this question of the composition of rates 
is one of considerable delicacy and importance, we shall here 
discuss it in detail. 

The general problem to be considered is as follows : — Having 
given the death-rate of the component parts of a population, to 
find what is the death-rate for the whole. 

Let a + b = total number of population (or body of men, as in 
preceding example), where a and b represent the population of 
each part. 

Also let X = death-rate per unit of the portion a, 

and 2/= „ _ „ „ „ &, 

Where x differs from y. 
Then the number of deaths in a = ax x = ax. 
Also „ „ „ b = hxy=^by. 

Therefore the total number of deaths in {a+b) = ax + by. 
Hence, dividing by the total population, we obtain — 

^ = death-rate per unit for the whole. 

a + b 

If the two parts of the population are equal ; i.e., if a = b, 

,11,1 , J- .^ 11 CIX + ay alx + y) x+y 

the death-rate for the whole = = -^;; — ^ == —~, 

a + a 2a 2 

which is the mean of the two rates x and y. 

Hence, when the parts of which a population is composed are 

equal, the death-rate of the whole is the mean of the death-rates 

of the component parts. 

But if a be twice as great as b; i.e., if a = 2b, then the 

r , ax + by 1 .,, 2bx + by b(2x + y) 2x + y 

formula ? may be written — - — _? = ^ „, ^^ = — — -^ 

a + b -^ 2b + b 2>b 3 

where evidently the death-rate for the whole is not the mean of 

the death-rates for the two parts. 

From this it is evident that Avhen the death-rates of the com- 



STATISTICAL FALLACIES. 335 

ponent parts of a population are given, the death-rate of the 
Avhole popuhxtion will depend on the relative proportion existing 
between the component parts of the population ; and any variation 
in these proportions will cause a corresponding variation in the 
total death-rate. In order, therefore, to ascertain the total death- 
rates from the death-rates of the parts, we must either know the 
actual population of each component part or their relative pro- 
portions. 

Reverting once more to the formula already given, viz., 

— ^ = death-rate i)er unit of the poiudation (a + h), it is 

a + h 

evident that, where the total death-rate is given and the death- 
rate of one component part of the population, this same formula 
will enable us to find the death-rate of the remaining portion. 

Thus, taking the example already quoted from the Times 
newspaper, 

The death-rate of the army at home and abroad in 1885 = 1L12 
per 1000. 

The death-rate of the army at home = 6 '68 per 1000. 

To find the death-rate of the army abroad. From the Registrar- 
General's returns, we find the strength of the total army in 1885 
= 198,064 ; of the army at home = 91,579 ; of the army abroad = 
105,748. 

-p ,, . 1 ax + by ,, TO 91579x6-68-1-105748x2/ 
By the formula -_^= 1M2= ^^^^^ , 

From which we obtain the result that y = 1 5 nearly. 
Similarly, having given the death-rate of the army in the 
United Kingdom in 1887 to be 5-3 per 1000, of the army abroad 
14-0, to find the death-rate of the total army, the strength of the 
army in the United Kingdom being 106,767, and of the army 
abroad 102,807. 

Death-rate of the whole army 

_ ax- -F % _ 106767 x 5-3 + 102807 x 14-0 
~ a + b 106767 -h 102807 

= 9-6. 

The use of the death-rate per 1000 instead of per unit in these 
calculations does not alter the result, as it aifects both numerator 
and denominator equally. 

Another example may be taken. Having given the population 
of the twenty-eight great towns (inoluding London) as 9,398,273, 



336 VITAL STATISTICS. 

and their deatli-rate per annum for the quarter ending December 
29th, 1888, as 19"8 per 1000, the population of London as 
4,282,921, and its death-rate for the same period 18-9 per 1000; 
to find the average death-rate for the other twenty-seven towns : — 

Let z = total death-rate, then — 

ax + h^i -. 
z = ~ ; whence 

ax + hy = z{a + b), 
hy = z(a + b) - ax, 
_ z(a + h) — ax 



y 



h 



rr.. f 19-8(4282921 +5115352)- 18-9x4228921 
^^^""^°^" y= — ^ 5115352 ' 

105138598-5 ^^ . 

=■ = 20-5. 

5115352 

Fallacies arising from stating Deaths in Proportion to Total 
Deaths. Tliese have already received consideration (pp. 124, 186). 
They present themselves under two heads. The deaths at one 
age are stated in proportion to the total deaths at all ages ; or the 
deaths from one cause are stated in proportion to the total deaths 
from all causes. In both cases the same fallacy is involved. A 
relationship is attempted to be established hetiveen two factors, 
both of tcMch are variable in value. An alteration in the total 
deaths on one hand, or in the deaths at one group of ages or from 
one cause on the other hand, might equally affect the proportion 
between the two, though the conclusions to be drawn in the two 
cases would by no means be necessarily identical. 



CHAPTER XXVIII. 



STATISTICS OF SICKNESS. 



WE have ip Chapter V. discussed the subject of registration of 
sickness, and have emphasized the importance of a more 
general registration of sickness, not confined to the chief infectious 
diseases. 

So far as the diseases notifiable under the Infectious Diseases 
(Notification) Act are concerned, there is gradually accumulating 
a valuable mass of information, which will become more valuable 
with every additional year. It is impossible here to summarize 
any of this evidence, but the following figures for London, derived 
from the Annual Report of the Medical Officer of Health of the 
Administrative County of London, may be taken as examples. 

Case-Rate per Million of Population. 





isin. 


1S92. 


1893. 


1894. 


1895. 


1896. 


Small-pox .... 
Scarlet Fever 

Diphtlieria .... 
Typhoid Fever 

Erysipelas .... 

Puerperal Fever, (a) case-rate ) 

per million of population 1 

(6) Case-rate per million births 


27 

2700 

1500 

800 

1130 

50 

1640 


100 
6400 
2000 

600 
1630 

80 

2550 


653 
8600 
3200 

900 
2260 

90 

2980 


274 
4300 
2600 

800 
1400 

60 

1920 


223 

4500 

2600 

800 

1300 

50 

1760 


50 

5700 

3100 

700 

1430 

60 

2040 



The notification returns have been utilized by Mr. Shirley 
Murphy to form some very suggestive tables as to the seasonal 
variations in age-distribution of scarlet fever, and the seasonal 
variations of fatality of diphtheria and of scarlet fever. 

The tables show that the children under five years of age who 
were attacked with scarlet fever in London, 1892-6, constituted 

z 337 



338 



VITAL STATISTICS. 



at the beginning and end of the year a larger proportion of the 
total number of persons attacked than at other times. 

The fatality from scarlet fever in London is highest in the early 
months of the year, declining generally in succeeding months to 
a minimum in September or October. Corrections made for 
difference in age and sex-distribution of the cases of each month 
appeared to show that these differences Avere insufficient to account 
for the above variations in the fatality. The figures supplied by 
diphtheria point in the same direction as those for scarlet fever. 



The materials are lacking for a complete study of the amount 
of illness in this country, in the absence of any complete 
system of registration of disease ; and estimates of the amount of 
non-infectious illness can only be based on the records of sick- 
clubs and benefit societies, and the official returns of the Army, 
Navy, and Police. 

JSTo distinct line of demarcation exists between health and 
sickness, and the two are connected by a series of intermediate 
states. Only sickness Avhich is sufficiently severe to involve 
confinement to bed or house, or to incapacitate for labour, is in 
practice capable of being registered; and even in regard to this 
disabling sickness our information is very partial. 

The following table, from the article by Dr. Farr in McCulloch's 
Account of the British Empire (1854), shows the time lost by 
sickness and by accidental injury among the labourers in Ports- 
mouth and Woolwich dockyards : — 





Mean 
Number 

of 
Workmen. 


Days Lost 

by 
Sickness. 


Days Lost 

by 

Accidents. 


Constantly 

Sick 
per cent. 


Constantly 
Suffering 

from 
Accidents 
per cent. 


Constantly 

111 
from both 

Causes 
per cent. 


Portsmonth 
Woolwich . 


5939 
2243 


27410 
10593 


15590 
8594 


1-26 
1-29 


0-73 
1-05 


1'99 
2-34 



The following table has been condensed from a similar table in 
a paper by Dr. J. Bertillon {Journal Royal Statistical Society, 
vol. Iv. part iv.). It gives a valuable summary of the sickness 
experience of Friendly Societies. 






O-Jf<i-IO(N000SC<IC<l-^ 






lOprHK)00rHO01(N7tl O 






oococo-^urjioooco 



OOOO»-l(N!N(MC0?D0'5 " 



lO>0'*0«0«0«>COi 



CO lO l» 00 CO tp 

o oj ^» t^ 00 i-H 






COt^T-l(NCOO(M<» 



Mln^-.opoo<^^Ol7^o 
oo^~^-.050.-lTt^t^ooKO 



g_3 s St) -5 
.£" fa rf S c ;= 



OOi-l5DCOOOI>-ipOO»OOi 

U5 iTj O 'X> t--. t-- OO «0 (r<I 00 
i-l 1-H T-H 



Ph a 
. o 






m »o «D t^ 00 1 






0.2 



«0 CO CD I-' 



irsOlrtOOOlOOi^OvTi 
(MCOCO-«<-*lOmCD50l^l^ 



I I I I I 



I I I I I 



I I < I I I I I t I I Jt *-i 

oiooknoiooooino'*?^ 

tNMcoco-sji-^inkcjcocot^ ^ 





340 



VITAL STATISTICS. 



The following table is derived from the Report on Sickness and 
Mortality Experienced in Registered Friendly Societies''' : — ■ 



Description and Nature of 
Experience. 


Exposed to 

Eisk of 
Sickness. 


Exposed to 
Eisk of 
Death. 


Average rate per annum 
in weeks 


Of 

Sickness. 


Of 

Mortality. 


Males (1856-60) . 
Females, England and Wales ) 
(1856-75) . . .] 
Wales, Males (1856-75) 
Males (1876-80) . 
Males (1861-70) . 


722338 

139122 

167255 
1662561 
1789532 


788891 

146793 

177897 
1662561 
1789532 


1-61 

2-34 

2-14 
1-89 
1-79 


•Oil 

•014 

•015 
•014 
•014 




4480808 


4565675 


1-83 


•013 



For the sickness statistics of the army and navy the reader 
is referred to the annual reports of the medical departments of 
these services. 

* Eyre and Spottiswoode, 10*. M. 



CHAPTEE XXIX. 

MISCELLANEA. 

aRAPHIO Methods. It liad been intended to write a 
special chapter dealing with graphic methods of stating 
statistical facts. Instead of this, illustrations of the method 
have been introduced throughout the book, which it is hoped 
will sufficiently prove the value of this method. The special 
application of the graphic method to the construction of a 
life-table is given on p. 266, and a similar method is described 
on p. 246 for cancer mortality. 

Certain cautions are required in applying the graphic method. 
By comparing curves, the scale of which is not identical, an 
erroneous conclusion has often been obtained. I am now speaking 
of diagrams constructed as parallelograms, of which the length 
{axis of the ahscissce) represents time, and the height [axis of the 
ordinates) represents mortality. A remarkable instance from 
Dr. Wallace's writings of the fallacy introduced by compressing 
the vertical scale of a diagram is given by Dr. McVail ( Vaccina- 
tion Vindicated, p. 2 et seq.). The fallacy introduced by such 
a reduction of the vertical scale can be demonstrated by 
ascertaining the average death-rate from a given cause for a 
series of years, and then stating the death-rate for each year 
as a percentage deviation from this average death-rate (Buchan 
and Mitchell's method). An example of this method is given 
in Fig. 25. 

Spot maps are frequently employed to indicate the incidence of 
infectious diseases in a town. It is doubtful if the maps of this 
description, published in the annual reports of the Metropolitan 
Asylums Board and of many medical officers of health, have more 
than a fractional value. They serve rather to indicate the density 
of population and the districts in which the largest proportion of 
children live, than the true prevalence of an infectious disease. 
Perhaps an exception may be made in the case of spot maps of 

341 



342 VITAL STATISTICS. 

the annual incidence of typhus, fever, as these would commonly 
indicate districts requiring the application of the Housing of the 
Working Classes Act. The true utility of a spot map consists in 
its employment in the office of a medical officer of health, where 
each case, plotted out as soon as it is notified, may serve to 
indicate the course of infection. 

Means and Averages. Throughout this work these terms have 
been employed as interchangeable and as indicating the arith- 
metical mean of a given series. It must be noted that if the 
mean of a series of death-rates a, b, c, d, and e is taken in 

accordance with the formula, arithmetical mean = ■, 

D 

an error is introduced if the number of deaths or of the 
population varies in the different years. llie only' accurate 
method is to add together the populations for each of the series 
of years, then the deaths in like manner, and from these deduce 
the mean death-rate for the entire period. (See footnote, p. 212.) 
In mathematics there are three other means, viz, : — 



the geometric mean, %/abcde, 

5 



the harmonic mean, 11111 
a n c d e 



and the quadratic mean, / ^ +" "^^ "^^ "*"^ - 

If the terms of the series are equal, the above means are all 

identical. If the terms are unequal, the quadratic mean is the 

highest, next the arithmetic, and then the geometric and harmonic 

means.* 

The value of a series of observations increases with the number 

of observations. The value of a given series may also be tested 

, ,,; , rr,, -c a + h a+h + c a + h + c + d, 

by taking successive means, ihus ir -— — , , ; 

2 3 4 

and so on be calculated, marked differences in means may be at 

first visible, but they become rapidly smaller with increasing 

length of the series if the series is a trustworthy one. The error 

of a given series is the deviation of its individual terms from its 

mean. The mean error in excess is the arithmetical mean of the 

* See papers on the " Importance and Value of Arithmetical Means," by 
Professors Radicke and Vierokdt {Neiv Sydenham Soc, vol. xi ). 



M-ISCELLANEA. 343 

errors of those terms above the mean of the series ; the mean 
error in (hficiencij, the arithmetical mean of the errors of those 
terms Lehnv the mean of the series ; while the mean error of the 
series is the average of these two. 

The probalde error is obtained by multiplying the mean error of 
the series (derived as above) by "67449 or by |-. The errors Avould 
fall short of this quantity as often as they would exceed it. 

The error of mean square is obtained from the quadratic mean 
as follows: — If ^ = quadratic mean, and a = arithmetical mean, in 
a series of ?i terms, then 

error or mean square = -t- . 

n'" - rt 

(For a full discussion of the above subject see Eadicke, op. cit., 
De Morgan's Essay on Probabilities, and Airy's Errors of Obser- 
vaiions, p. 18 e^ seq.) 

For a statement of Poisson's formula see p. 323. 

Fatality. The case-mortality, or fatality of patients, must be 
stated in proportion to the number of cases treated. 

The usual plan is to divide the deaths multiplied by 100 by 
half the sum of the admissions, discharges, and deaths for the 
year, or the period of inquiry. The importance of classifying 
patients according to age must not be overlooked. 

Probability of Eecurrence of a Disease apart from Infection. 

In attempting to solve problems as to the special incidence of a 
particular house or group of houses, e.g., phthisis or cancer, there 
are serious fallacies, unless special precautions are taken. First, 
there is the question of chance. It may be a mere coincidence 
that successive cases of, let us say, cancer have occurred in a 
particular dwelling. De Morgan showed that if a sufficient 
number of persons were set to work tossing pence, one of these 
persons would eventually, if he continued the operation for a 
sufficient length of time, turn up " heads " for a thousand times 
in succession, without a single interval of "tails." It is plain, 
therefore, that the fact that several successive families living in a 
house have each had members suffering in this house from cancer, 
does not necessarily prove a causative relationship between the 
condition of the house or of the soil on which it is built, and the 
origin of the disease. 

Secondly, there is the question of age-incidence. The tendency 
to cancer increases rapidly with advancing years. As according 



344 A^ITAL STATISTICS. 

to Dr. Ogle's calculations at least one out of twenty-one men and 
one out of twelve women who reach the age of 35 eventually die 
from cancer, it would be surprising if in residential towns and 
districts there did not frequently occur a succession of deaths 
from cancer in a particular house or group of houses. Careful 
correction must be made for age-distribution of the population, 
and the amount of cancer in the houses investigated shown to be 
very markedly in excess of that in others, before any influence of 
locality or house-infection can safely be predicated. 

Dr. JSTiven, in his annual report for the city of Manchester for 
1897, gives the following investigation of the house-incidence of 
enteric fever, in which (apart from the question of age-incidence, 
which probably does not seriously affect the conclusions in this 
case) correct methods are pursued. 

He first assumes that all the houses in the city are equally 
liable to invasion. Then, excerpting the average number of 
houses affected once in the seven years, the chance of any one 
house being affected in any one year is 

_ Average number of houses affected 
Average number of occupied houses* 
Let m be the number of years over which the inquiry extends. 
The chance of any house being affected in two different years is 

^— ^' and the chance of a house being thrice invaded in 

x^hiItix 1^ I'm ^^ 

separate years is !^ -L^ -> . The number of houses 

o 

which we should expect to be invaded on these suppositions is : — 
Affected twice, ^ •'' x average number of occupied houses in 

the city; affected thrice, ^M'>^^ - ^) i'>n - 2) ^ ^^^^^^^ num}i(,i of 

occupied houses in the city. 

AT 490 , 

106721''^^- 

X'Yyh (yyi \\ 

Hence \^ 1 x average number of houses = 47 "2. 

The actual number twice invaded is 78. The excess of actual 
over the calculated recurrences is thus 31, or if we reckon the two 
double recurrences, 33. '^M^ - 1) jin-'i) ^ ^^^ number of 



MISCELLANEA. 345 

houses = 0'35, while the actual number of recurrences three times 
is 2. It will be seen, then, that there is an excess of actual 
recurrences, but not a great and striking excess. It may be 
doubted, however, whether the persistence is to be looked for so 
much in the house itself as in neighbouring houses, assuming that 
it is due to growth of infective matter in the soil outside the 
house. 

Then, moreover, we should perhaps expect the excess to be 
more marked if we take successive years. i» 

The expectation of recurrence in successive years, the number 
of the years being seven, is 6x^, and the number of such expec- 
tation recurrences is 13-5. The number of actual recurrences is 
20. Here also, then, there is an excess of the actual over the 
expectation recurrences. 

Dr. Niven concludes that the facts would probably yield more 
evidence if examined in a more elaborate manner. Thus, for 
example, the list of recurrences show a special tendency to 
recurrence in "West Gorton, and a separate calculation for that 
district would probably yield more evidence of persistence. On 
the other hand, the calculation will not stand small figures, being 
essentially of a rough character, and subject to material deductions 
on the ground of doubtful diagnosis. 

Calculation of Population of Sub-Districts. When the popu- 
lations of a town or district and of its constituent sub-districts are 
calculated by the Registrar-General's method, the summation of 
the latter is not equal to the former. The correct populations for 
the sub-districts may be obtained by the use of the following 
formula given by Dr. L. Parkes (Public Health, vol. v. p. 191). 
First, the populations of the district and of its sub-districts are 
calculated by the Registrar-General's method (p. 6). 

Then, if P= estimated population of entire district in 1898, 
and 7? = census „ „ „ 1891; 

and if P^, P^, Pg = 

estimated populations of the constituent sub-districts in 1898, 
and p^, p^, p^--^ 

census populations of the constituent sub-districts in 1891, 

then P=-^ P+^ P+P^ P, 
2? p) p 

where ^iP '-^P and -^sp 
p p p 

are the correct populations of the three sub-districts in 1898. 

Z2 



346 VITAL STATISTICS. 

Aids to Calculation. It is assumed throughout that the 
student is familiar with the use of tables of logarithms. I have 
found Jackson's Accented Five-figure Logarithms (W. H. Allen 
and Co.) very useful, as with these it is unnecessary to calculate 
diilerences. For the majority of the calculations required in 
medical statistical work, Crelle's Multiplication Tables, or the 
Direct Calculator of M. B. Cotsworth (York, 21s. nett) are more 
expeditious than logarithmic tables, and simply invaluable for 
every-day-Avork. Fuller's Slide Rule is also useful, but in my 
experience is not so convenient as Crelle's or Cotsworth Tables. 



POSTSCEIPT. 



The Bertillon Classification of Causes of Death. While this 
Edition is passing through the press, the author's attention has been 
drawn to this system, which is about to be adojsted in the United 
States, Canada, and Mexico, and j^ossibly in other countries, as well 
as France. It has an anatomical basis, like Farr's classification, and 
can be employed so as to include 40 diseases, or 89, or 142, according 
as a less or more complete classification is required. The three arrange- 
ments are arranged so that statistics obtained under any one of the 
three are comparable. 



INDEX. 



Accident : in ditferent occupations, 
181 ; causes of deatlis from, 253 

Ages: misstatements as to, 2 ; absence 
of statement of in Loudon inter- 
mediate census, 9 ; at marriage, 61 ; 
in relation to fecundity, 66 ; death- 
rate at different, 117 ; incidence of 
small-pox at different, 215 

Air: effects of breathing foul, 157, 
181 ; dust-laden air, 182 

Alcoholism : in different occupations, 
184 

Aneurism : in different occupations, 
180 . 

Ansell : on age at marriage, 61 

Arithmetical mean progi'ession, 5 

Average death-rates : fallacy of, 191; 
as to puerperal fever, 232 ; errors 
of, 327 

Average strength : errors in connec- 
tion with, 329 

Averages: varieties of, 342; probable 
error of means, 343 

Back-to-back houses, 166 

Balfour, T. G. : on incomparability of 
data, 325 

Barry : on back-to-back houses, 166 

Berlin : monthly incidence of births, 
76 ; illegitimacy in, 83 

Bertillon, J.: on legitimate and ille- 
gitimate birth-rates, 64 ; on birth- 
rate according to social position, 
75 ; on age composition of popula- 
tion in European countries, 95 ; on 
statistics of Friendly Societies, 339 

Birth-places : of population of cities, 
11 : of population of England and 
Wales, 12 



Births : to a marriage, 69 ; registra- 
tion of, 19 ; still births, 23, 79 ; 
defects in registration of, 73 ; pro- 
portion of male and female, 81 ; 
illegitimate, 82 

Birth-rates : method of estimation, 
71 ; national and international, 73 ; 
decline of, 74 ; causes of decline of, 
77 ; of urban populations, 74 ; in- 
fluence of social position on, 75 ; 
influence of prosperity, and nation- 
ality, 76, 77 ; influence on death- 
rate, 92 ; influence on infantile 
mortality, 133 ; influence on mean 
age at death, 294 

Bodio : on emigration, 13 

Brighton : influence of visitors on 
death-rate of, 89 ; life-table of, 261, 
275 

Bright's disease : in different occupa- 
tions, 181 

Bristowe : on relation between birth- 
rate and duration of life, 295 ; 
formula of, 301 

Bronchitis : in diflTerent occupations, 
180 

Buchan and llitchell : grapliic 
method, 341 

Budapesth: tables of natality for, 66 

Calculations : aids to, 346 

Cameron, R. W. D. : on birth-rate 
and death-rate, 98 

Cancer: in ditferent occupations, 179; 
death-rate from, 241 ; arguments 
as to apparent increase, 242 ; local 
distribution of, 248 ; heredity in, 
248 

Cannan, E.: on migration, 10 



348 



VITAL STATISTICS. 



Carlisle life-table, 287 
Case-mortality. See Fatality 
Causes of death : fallacies in registra- 
tion of, 29 ; ill-defined, 29 
Census: history of, 1 ; age and sex 
enumeration, 2 ; errors in data, 2 ; 
quinquennial , 8 ; cost of, 9 ; inter- 
mediate in London, 9 ; definition 
of house and tenement, 160 
Chadwick, E. : fallacies as to birth- 
rate, 75 ; on relation between age 
of living and at death, 297 
Cholera: varying fatality of, 37 
Circulatory diseases : death-rate from, 

251 
Classification of diseases, 34 
Climate: influence on death-rate, 137 
Coghlan : on child - birth statistics, 

234 
Collins: dissent from vaccination 

report, 208, 220, 222 
Comparative mortality figures, 108 ; 

in different occupations, 175 
Corfield : on mean length of life, 296 
Counties: relative migration from, 11 
Cyclical changes in disease, 146 ; 
waves, 189 

Death-rate; estimation of, 85 ; for 
short periods, 85 ; crude and special, 
87 ; effect of migration, 87 ; of 
public institutions, 89 ; official cor- 
rections of, 91 ; influence of birth- 
rate on, 92 ; special instance of 
do., 99 ; influence of age and sex 
on, 102 ; method of correction of, 
trustworthiness of general. 111 ; 
at age-periods, 115 ; infantile, 120 ; 
influence of climate and season, 
136 ; of cyclical changes, 146 ; of 
race, 147 ; of marital condition, 
149 ; of sanitation, 149 ; of density 
of population, 153, urban and 
rural, 155 ; influence of occupation, 
171 ; from special diseases, 185 et 
seq.; standard, recorded, and cor- 
rected, 108 ; danger of average, in 
infectious diseases, 191 ; decline in 
the English, and causes, 315 

Death-certification : recommendations 
as to, 25 ; improvements required, 
26 



Deaths: uncertified, 24 

De Moivre's hypothesis, 287, 297 

Density of population: method of 
calculating, 153 ; relation to mor- 
tality, 154 ; causes of high mor- 
tality with increased, 157 ; true 
test of, 135, 159 ; effect of higher 
degrees of upon mortality, 162 

Developmental diseases: death-rate 
from, 250 

Diabetes: death-rate from, 249 

Diarrhoea: seasonal incidence of, 139; 
criticism of official method of stat- 
ing death-rate from, 188 ; death- 
rate from, 204 

Dickens, C. : on sickness registration, 
38 

Dickson : on sickness registration, 38 

Dietetic diseases: death-rate from, 
249 

Diphtheria: seasonal incidence of, 
143 ; and law of periodicity, 147 ; 
death-rate from, 196 ; fatality of, 
198 

Drage: on trans-oceanic emigration, 
13 

Dropsy : transference of, 32, 252 

Drysdale: fallacies as to relation of 
birth-rate to death-rate, 99 ; as 
to low mean age at death, 158 

Duration of life : methods of calculat- 
ing, 291 ; probable, 297 

Dust-laden air: eff'ect of in occupa- 
tions, 183 

Emigration : See p. 9 ; machinery in 
Ireland, 10 ; trans-oceanic, 13 

Enteric fever: seasonal incidence of, 
144 ; death-rate from, 200 ; fatality 
of, 203 ; altered age incidence of, 
220 

Enteritis: relation to epidemic 
diarrhoea, 204 

Estimates of population: methods, 
5 ; Eegistrar-General's, 5 ; from 
birth-rate, 7 ; from number of in- 
habited houses, 7 ; criticism of 
official, 8 

Expectation of life : curtate and com- 
plete, 276, 298 ; according to 
various life-tables, 299, 300 ; 
changes of in England, 304 



INDEX. 



349 



Factor for correction of death-rate, 
108 

Factory and Workshops Act : notifi- 
cation of sickness nnder, 44 

Fallacies: in registration of cansesof 
death, 29 ; as to average death- 
rates, 54 ; as to fatalit3% 54 ; as to 
age-distribution of jiopulation, 54; 
as to occupational mortality, 174 ; 
from smallness of data, 185 ; aris- 
ing from variations of virulence of 
disease, 186 ; of average death- 
rates, 191 ; of mean age at death, 
171, 294; classification of, 322; 
from paucity of data, 323 ; from 
inaccuracy or incomparability of 
data, 325 ; of averages, 327 ; of 
hospital statistics, 330 ; from com- 
position of ratios, 333 ; from stating 
deathsin proportion to total deaths, 
336 

Farr: census work, 1 ; as father of 
sanitary science, 9 ; on delay in 
issuing reports, 28 ; on value of 
reports, 28 ; on doubtful cases of 
death, 34 ; on grouping of ages, 
117 ; on illegitimacy and infantile 
mortality, 131 ; on relation between 
density of population and mor- 
tality, 154 ; on zymotic diseases, 
189 ; on life-table as biometer, 255 ; 
notation of, 258 ; formula of as to 
duration of life, 301 ; on sickness 
among Government labourers, 338 

Fatality of disease: relation to pre- 
valence, 37 ; variations with age, 
185 ; of measles, 192 ; of scarlet 
fever, 195 ; of diphtheria, 198 ; of 
enteric fever, 203 ; of small-pox, 
225 ; method of calculating, 343 

Fecundity : age in relation to, 66 

Fever, See Enteric fever and Typhus 

France: causes of decline of birth- 
rate in, 77 ; relation lietween birth- 
rate and death-rate, 97 

Friendly Societies : utilisation of sta- 
tistics of, 44 

Galton, F. : on isogenes, 69 
Geometrical mean progression, 6 
GifFen, R. : on condition of wage- 
earning classes, 317 



Gloucester: deaths from small-pox in, 
209 ; fatality of small-pox in, 227 ; 
attack-rate in, 229 

Gout: in different occupations, 179 

Graphic method of constructing life- 
table, 265 ; of obtaining annual 
from mean death-rates, 246 ; cau- 
tions as to, 341 ; spot maps, 341 

Gresswell : on inverse relation between 
scarlet fever and rainfall, 234 

Guy: on small-pox epidemics, 211 ; 
on errors of averages, 327 

Haldane: on air impurity in houses 
of different sizes, 157 

Halley : first English life-table, 286 

Hamburg: still-births at, 23 ; monthly 
incidence of births, 77 ; infantile 
mortality of, 130 

Hayward : on method of obtaining 
population 0-5 for life-table, 271 ; 
description of improved short 
method of constructing life-table, 
278 

Healthy Districts Life-table: basis of 
facts, 152, 288, 289 

Heart, disease of: in different occu- 
pations, ISO 

Hoffman: on effect of race on mor- 
tality, 147 

Hooker: modes of census taking, 2 

Hospital statistics: importance of 
utilising, 42 ; fallacies of, 330 ; as 
to bed death-rates, 332 

Huddersfield : as example of abnormal 
age distribution of population, 104 

Illegitimacy: method of estimating, 
82 ; in England, 83 ; in other 
countries, 83 ; influences on in- 
fantile mortality, 130 

Infantile mortality, 121 ; do, in each 
month of first year, 121 ; in dif- 
ferent countries, 130 ; effect of 
illegitimacy on, 130 ; in relation to 
insurance, 132 ; influence of birth- 
rate, 133 ; of density of population, 
134 

Infant Life Protection Act, 132 

Infectious diseases, notification of, 
47 ; provision of Act, 48 

Influenza: altered age-incidenceof,222 



350 



VITAL STATISTICS. 



Inquests: law as to, 24 ; in relation 
to death-registration, 25 

Insurance: in relation to infantile 
mortality, 132 

Intemperance: and density of popu- 
lation, 159. See Alcoholism and 
Liver Diseases 

Isogenes, 69 

Jones, H. R. : on relation between 
birth-rate and infantile mortality, 
134 

Jones, Herbert : on back-to-back 
houses, 167 

Kelly, C : on low death-rates, 87 ; on 

factors of correction, 112 
King, Geo.: on cancer statistics, 242; 

on graphic method of constructing 

life-table, 265 
Korbsi: on tables of natality, 66; on 

standard populations, 114 ; on 

small-pox death-rates, 214 

Lead poisoning. See Plumbism 

Leicester: age-incidence and fatality 
of small-pox in, 224, 226 ; attack- 
rate do. , 228 

Letheby: fallacious statements as to 
relation of birth-rate and death- 
rate, 96 

Life capital, 310 

Life-tables: as biometer, 255; de- 
scription of, 256 ; method of con- 
struction of, 267 ; details of con- 
struction, 261 ; short method of 
constructing. 279 ; Northampton, 
287 ; Carlisle, 287 ; English, 288 ; 
healthy districts, 288 ; of various 
great towns, 300 

Littlejohn, H. : on fatality of measles, 
192 

Liver diseases: in different occupa- 
tions, 181 ; death-rates from, 250 

Liverpool : erroneous estimated popu- 
lation, 8 

Local Government Board : in relation 
to sickness registration, 55 

London : quinquennial census of, 9 

Longstaff : on causes of migration, 12 ; 
on inverse relationship between 
scarlet fever and rainfall, 234 



Malignant disease. See Cancer 

Malthusian hypothesis, 83 

Manchester life-table, 308 

Marriages : estimation of rate of, 56 ; 
condition as to of English popula- 
tion, 58 ; of other countries, 58 ; 
in towns, 59 ; influence of national 
prosperity on, 59 ; decline of, 60 ; 
calendar of, 60 ; re-marriages, 60 ; 
ages at, 61 ; of minors, 62 ; signa- 
tures in register, 63 ; fecundity of, 
65 ; reduction of rate in relation to 
growth of population, 66 

Married life : duration of, 69 ; in- 
fluence on mortality, 149 

McVail : on report of Royal Commis- 
sion on Vaccination, 208 ; on 
small-pox, 211 ; on influence of 
deaths from chicken-pox on small- 
pox death-rates, 215 ; on intervals 
iDetween small-pox epidemics, 219 

Mean after-lifetime. See Expectation 
of life 

Mean age at death : relation to other 
tests of duration of life, 290 ; in 
different occupations, 171 ; fallacies 
of, 294 ; effect of birth-rate on, 294 

Mean duration of life, 298 

Mean length of life, 296 

Means. See Averages 

Migration: effect on population, 9 ; 
internal, 10 ; between urban and 
rural districts, 10 

Milne : Carlisle life-table, 287 ; method 
of, 265 

Murcliison : on fatality from typhus 
fever, 186, and from enteric fever, 
203 

Measles : seasonal incidence of, 141, 
193 ; nunor and major epidemics 
of, 190 ; death-rate from, 191 ; 
fatality of at different ages, 192 

Natural increase : of English popula- 
tion, 9, 84 ; of other countries, 15 

Nervous diseases: death-rates from, 
251 

Newcastle-on-Tyne : erroneous esti- 
mated population, 8 

New Zealand : death-rate of, 88 

Niven : on house incidence of enteric 
fever, 344 



INDEX. 



351 



Nomenclature : of diseases, 34 ; lack 
of unifoiniity, 30 

Northampton life-table, 287 

Norwich: as an example of an im- 
usiial age-distribution of popula- 
tion, 104 

Notification of sickness : proposals as 
to, 42 ; under Factory and Work- 
shops Act, 45 ; compulsory notifi- 
cation of infectious, 47 ; provisions 
of Act, 48 ; advantages of, 51 ; 
effect of upon zymotic mortality, 
53 ; suggestions as to, 55 ; in Ger- 
man}' and Scandinavia, 56 

Nottingham : erroneous estimated 
population, 8 

Occupations and mortality, 169 ; 
classification of, 170 ; methods of 
comparison between, 171 ; errors 
in statistics of, 175 ; mortality 
according to causes, 177 

Ogle : on census data, 2, 5 ; on divi- 
sion between urban and rural 
districts, 11 ; decennial supplement, 
28 ; on marriage-rate and growth 
of population, 66 ; on influence of 
age and sex-distribution on death- 
rate, 102 ; on true comparison 
between rural and urban death- 
rate, 112; on international standard 
death-rates, 113, 114 ; on opera- 
tion of Farr's law, 157 ; on effect of 
coal dust, etc , 183 ; on small-jjox 
death-rates, 217 ; on cancer deaths 
at different ages, 344 

Old age : death-rate from, 251 

Overcrowding: standard of, 161 ; in 
different districts, 160 

Parkes, L. : on relation between 
diarrhoea and enteritis, 204 ; cal- 
culation of population of sub- 
districts, 345 

Peabody Buildings : true test of den- 
sity of population, 135, 159 ; in- 
vestigation as to, 165 

Periodicity and disease, 146 ; of 
epidemic diseases, 189 

Phthisis : in different occupations, 
179 ; death-rates from, 237 ; local 
distribution of mortality from, 



240 ; relation between sickness and 
deaths, 316 

Physicians, Royal College of: nomen- 
clature of, 34 

Playfair : on registration of sickness, 
37 

Plnmbism : in different occupations, 
181, 183 

Pneumonia : in different occupations, 
180 

Poisson : formula of, 323 

Population : basis of statistics, 1 ; 
enumeration of, 1 ; errors in enu- 
meration, 2 ; estimates of, 5 ; criti- 
cism of estimates of, 8 ; effect of 
migration on, 9 ; birth-places of, 
12 ; from an international stand- 
point, 15 ; natiu-al increase of, 9 
and 84 ; density of population, true 
test of, 135 

Portsmouth : ei-roneous estimated 
population, 8 

Preventive medicine : scope of, 41 

Price : on Northampton life-table, 
287, 294 

Probabilities: in relation to death- 
rate, 259 ; of life, 302 ; of recur- 
rence of disease apart from infec- 
tion, 343 

Prosperity : influence on marriage- 
rate, 59 ; on birth-rate, 76 

Public institutions : as affecting 
death-rate, 89 

Puerperal fever: definition of, 231 ; 
death-rate from, 232 ; fallacy of 
average death-rates as to, 232 

Pye-Smith: on "over-pressure," 317 

Quinquennial census, 8 ; of London, 9 

Race: influence on death-rate, 147 

Radclifle, N. ; on law of periodicity, 
146 

Rainfall : deficiency of in relation to 
diphtheria and other diseases, 234; 
inverse relationship to diabetes, 249 

Ransome: on variation of death-rate 
caused by age, 105 ; on fallacious 
method of stating deaths from a 
given cause, 186 ; on cyclical waves, 
189; on death-rate from tubercular 
diseases, 237 



352 



VITAL STATISTICS. 



Registrar : relation to medical officer 
of health, 22 

Registrar-General: method of esti- 
mating population, 5; enumeration 
of reports of, 27 ; method of correc- 
tions, 91, 105 ; on death-rate from 
seven chief infectious diseases, 189; 
on limitation of utility of statistics, 
252 

Registration: of births and deaths, 
18 ; history of, 18 ; law as to, 20 ; 
use made of information furnished 
by, 27 ; of causes of death, 29 ; of 
sickness, 37 ; defects in registra- 
tion of births, 73. See also under 
Sickness and ISTotification 

Re-marriages: 60 

Reports: of Registrar-General, 27 

Respiratory organs, diseases of: re- 
duction in death-rate from, 239 

Rheumatic fever: hospital statistics 
as to, 43 ; in different occujaations, 
79 

Richardson, B. W. : on death-rate of 
"Hygeiopolis," 295 

Rumsey : on mean age of living, 
296 

Rural districts : migration from, 10 ; 
mortality of, 155 

Russell: on notification of sickness 
to a layman, 46 ; on density and 
mortality, 162 

Salford : erroneous estimated popula- 
tion, 8 

Sanitation: influence on death-rate, 
149 

Scarlet fever: seasonal incidence of, 
142 ; death-rate from, 193 ; rela- 
tion between prevalence and fatality 
of, 194 

Seasonal incidence : of disease, 137 ; 
of zymotic and other diseases, 138 
et seq.; also 193, 206 

Sex : proportion of males and females 
at birth, 81 ; effect on mortality, 
117 

Sickness: registration of, 37 ; at- 
tempts made, 38 ; requirements of 
a plan, 39 ; information available, 
40 ; proposals as to notification of, 
42 ; compulsory notification of in- 



fectious, 47 ; statistics of, 337 ; in 
Friendly Societies, 339 

Small-pox : seasonal incidence of, 
1% 139 ; and law of periodicity, 146 ; 
statistics of, 209 ; in pre-registra- 
tion period, 211; in 1870-71, 211; 
in foreign countries, 213 ; age in- 
cidence of mortality from, 215 ; 
alteration of same, 220 ; local 
variations of age incidence, 222 ; 
fatality of, 225 ; attack-rate from, 
228 

Social position: influence on birth- 
rate, 75 

Standard : death-rate, 108 ; million 
of population, 119 ; population for 
occupational mortality, 173 

Still-births: no records in England, 
23 ; law as to, 23 ; statistics of 
other countries, 23, 79, 80 

Suicide : in different occupations, 
181 ; different forms of, 253 ; in 
different countries, 254 

Sweden : first census, 1 ; periodicity, 
of epidemic diseases in, 189 ; small- 
pox in, 213 

Tabes mesenterica: vague character 
of, 239 

Tatham : decennial supplement, 27 ; 
and national registration of infec- 
tious diseases, 54 ; on crude and 
corrected death-rates, 112 ; on 
back-to-back houses, 166 ; on age 
incidence of mortality from phthisis. 
237 ; on changes in expectation of 
life, 305, 309 ; on life-capital, 310 

Thomson, T.: on fatality of measles, 
192 

Tubercular diseases : death-rate from, 
236 

Tuberculosis : supposed confusion 
with "fever," 220; transference 
from phthisis, 239 

Typhoid fever. See Enteric fever 

Typhus fever: fatality according to 
age, 185 ; death-rate from, 200 ; 
altered age-incidence of, 220 

Uncertified deaths, 24 
United States : increase of population 
of, 18 ; birth-rate in, 65 



INDEX. 



353 



Urban districts: migration into, 10 ; 

birth-rate of, 74 ; death-rate of, 

155 
Urinary diseases: death-rate from, 

252 

Vaccination : in relation to small- 
pox, 218 ; summary of report of 
Royal Commission on, 230 

Violence: death-rate from, 252 



Whitelegge: on periodicity in epi- 
demic diseases, 189 

Whooping-cough : seasonal incidence 
of, 141 ; death-rate from, 200 

Wilbur : on fecundity of marriage, 65 

Willich : formula of, 301 

Zymotic diseases: enumeration of, 
41 ; methods of stating death-rate 
from, 185 



PLYMOUTH : 

WILLIAM BRBNDON AND SON, 

PRINTERS. 



£r THE SAME AUTHOR. 



EPIDEMIC DIPHTHERIA: 

A KESEARCH ON THE ORIGIN AND SPREAD OF THE 
DISEASE FROM AN INTERNATIONAL STANDPOINT. 

1898. 7s. M. 



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